\ r

The use of intra-subject variability as a means of identifying

performance enhancement interventions*

By

Gary Park BA, BSc

Supervisor

Dr Kieran Moran

A thesis submitted in fulfilment o f the degree of

MSc Biomechanics

October 2005

School o f Health and Human Performance, Dublin City University

I

DCU

I hereby certify that this material, which I now submit for assessment on the

programme of study leading to the award of Master of Sceince Degree in

Biomechanics is entirely my own work and has not been taken from the work of

others save and to the extent that such work has been cited and acknowledged within

the text of my work.

ID No.: 91169436

II

Acknowledgements

Firstly, I would like to thank all the subjects that took part in the study, especially

those that additionally were part of the pilot work needed

1 would like to thank Kieran for his help and patience, for his calmness, understanding

and guidance

I extend thanks to Ben and Albert for their input and clarification on technical aspects

Thanks also to Neil for his advice and a place to stay on my many trips to the library

in Liverpool Thank you to Phil for his help and philosophical advice, putting things

in perspective and help in finding a path through problems

Most of all I would like to thank my family Their continued support, patience and

understanding over the last few hard years Their love and giving all my life is far

beyond anything that could be expected or dreamed of My appreciation for what

they have always done for me goes beyond words

I I I

Table of Contents

Introduction ••••••••••••••••••••••••••* •••• • ••••••••••••••••••••••• •••••• • •• • ••••••••• •••• 1

1 1 Rational 2

1 2 Hypothesis 4

13 Limitations 5

Review of L iterature....................................................................................... 6

2 0 Introduction 7

2 1 Variability 8

2 1 1 Variability in movement 8

2 1 2 Movement control theories 9

2 1 3 Variability in Biomechanics studies 11

2 1 4 The use of variability in movement assessment 14

4 1 5 Group analysis verses individual subject analysis 18

2 2 Biomechanics of vertical jumping 20

22 1 Vertical jump mechanics 21

2 2 2 Whole body kinematics 22

2 2 3 Whole body Kinetics 23

2 2 4 Segmental kinematics 27

2 2 5 Segmental kinetics 28

2 2 5 Relative segmental contribution 33

2 26 Rate of force development (RFD) 35

2 2 7 Enhancement of jump height due to countermovement 38

2 2 7 1 Enhancement of mechanical variables 39

2 2 7 2 Possible mechanisms for enhancement 40

2 3 Coordination 44

2 3 1 Constraints influencing movement pattern 45

2 3 2 Biarticular muscles 50

2 3 3 Coordination in Vertical jump 51

2 3 3 1 Pattern of joint extension 52

2 3 3 2 Timing of peak angular velocity 54

2 3 3 3 Timing of peak joint power 56

2 3 4 Coordination as a predictor of jump height 57

IV

2 4 Training interventions to increase jump height 58

2 4 1 Training methods to improve neuromuscular capacity 60

2 4 2 Changes in kinetic parameters in drop jumps 62

2 4 2 1 Drop jump technique 63

2 4 2 2 Drop jump height 67

2 4 3 Drop jump training studies 70

Methodology............................................................................................. 7331 Subjects 74

3 2 Experimental protocols 74

3 3 Data Acquisition 76

3 4 Data analysis 77

3 5 Variable selection 80

2 6 Statistical analysis 83

Results ..................................................................................................... 844 1 Variability and the relationship with jump performance 87

4 1 1 Jump predictors based on group analysis 99

4 1 2 Selection of jump parameter to alter to enhance jump height 100

4 1 3 Variability and parameter identification 102

4 2 Coordination and jump performance 103

4 3 Rate of force development and CMJ performance 105

4 4 Comparisons of kinetics between the CMJ and the DJ 108

Discussion............................................................................................... 1145 1 Inter-subject verses Intra-subject variance 115

5 2 Group analysis 116

5 3 Comparison between group and individual level 119

5 4 C oordination 122

5 5 Inter-subject analysis verses Intra-subject analysis 123

5 7 The use of drop jumps as a means of training the CMJ 130

5 8 The suitability of drop jump as a means of training the CMJ 132

5 9 Conclusion 133

510 Future research 134

References.............................................................................................. 136

Appendix..................................................................................................XI

V

List of TablesTable 2 1 Coefficient of variance (CV) [%] of initial impact forces in selective

landing actions 11

Table 2 2 CV [%) of stride length during running at various running velocities12

Table 2 3 Inter-subject and intra-subject standard deviation [m] and CV[%] for height attained in the CMJ 12

Table 2 4 CV [%] of duration of concentric phase in the CMJ . 13

Table 2 5 Inter-subject CV[%] of segmental data for the CMJ (van Soest et al, 1985) 13

Table 2 6 Inter-subject CV [%] for joint moment and power in the CMJ 13

Table 2 7 Duration of the eccentric and concentric phases of the CMJ 23

Table 2 8 Average whole body vGRF and vertical impulse during concentric phase of the CMJ 23

Table 2 9 Peak vGRF during vertical jumping 25

Table 2 10 Total work done during the concentric phase » 26

Table 2 11 Peak joint angle during vertical jump 28

Table 2 12 Peak angular velocity of joints during concentric phase 28

Table 2 13 Peak joint moments during concentric phase of CMJ 29

Table 2 14 Joint moments at time of joint reversal in the CMJ 31

Table 2 15 Peak joint power during concentric phase of the CMJ 31

Table 2 16 Absolute amount of work performed by the joints during theconcentric phase in the CMJ 33

Table 2 17 Relative contribution of each joint to total work during concentric phase of the CMJ 34

Table 2 18 Timing of joint reversal to take-off (absolute and relative to totalduration) 52

Table 2 19 Mean timing of peak joint velocities (absolute and relative to total duration) . . 55

Table 2 20 Mean timing of peak joint power prior to take-off (absolute andrelative to total duration) , 56

VI

Table 2 21 Comparison of whole body concentric phase parameters between CMJ and DJ for the two groups in the study by Bobbert et al (1986a) study and the three conditions in Bobbert et al (1987a) 63

Table 2 22 Kinematic and kinetic output of CMJ and DJ (Bobbert et al, 1986a)64

Table 2 23 Mean kinematic and kinetic variables from CMJ and DJ (20cm) 66

(from Bobbert et al, 1987a) 66

Table 2 24 Effect of drop jump training on CMJ performance 71

Table 3 1 Cut off frequencies of each joint marker (Moran, 1998) 77

Table 4 1 Mean and variance values of whole body kinematics and kinetics for the group and average variance for individuals during the eccentric phase

87

Table 4 2 Correlation (r) and level of significance (p) for the relationship between jump height and whole body kinematics and kinetics during the eccentric phase 88

Table 4 3 Mean and variance values of joint kinematics and kinetics during the eccentric phase for the group and average variance for individuals 89

Table 4 4 Correlation (r) and level of significance (p) for the relationshipbetween jump height and selected segmental parameters during eccentric phase 90

Table 4 5 Mean and variance values of whole body and segmental kinematics and kinetics for the group and average variance for individuals at the start of the concentric phase 91

Table 4 6 Correlation (r) and level of significance (p) for the relationshipbetween jump height and kinematic variables at the start of the concentric phase 93

Table 4 7 Group mean, SD and CV and individual SD and CV for whole body kinematics and kinetics for during the concentric phase 94

Table 4 8 Correlation (r) and level of significance (p) between jump height and whole body kinematics and kinetics during the concentric phase 95

Table 4 9 Mean and variance of segmental kinematics and kinetic for group and average variance for individuals during the concentric phase 95

Table 4 10 Correlation (r) and level of significance (p) between jump height and segmental kinematics and kinetics during the concentric phase 97

Table 4 11 Percentage of total work done by each joint and correlation withjump height 98

V II

Table 4 12 Descriptions of relationship between jump height and mechanical parameters that where correlated at a group level and number of individuals that also exhibited a correlation with jump height for these parameters 99

Table 4 13 Mean, variance and slope for selected parameters to highlight issue regarding selection parameters to altering to achieve increases in jump height 101

Table 4 14 Mean, standard deviation and range of jump height observed for each individuals and the number of significant relationships observed 102

Table 4 15 Mean timing of joint pairings for key events and measures of mter- subject and intra-subject variability 103

Table 4 16 Mean and variance values of RFD of ankle, knee and hip jointmoments, and whole body vGRF . 105

Table 4 17 Correlation (r) between jump height and (1) rate of forcedevelopment and (11) power development over selected intervals 107

Table 4 18 Differences in jump height achieved and whole body kinematics and kinetics between CMJ and DJ from 0 3m and 0 5m 109

Table 4 19 Differences in joint kinetics between CMJ and DJ from 0 3m and 0 5m 111

Table 4 20 Kinetic parameters overloaded in the DJ compared to the CMJ, with parameters significantly correlated with jump height in CMJ indicated 113

Table 5 1 Representation of possible scenarios between group and individual analysis . 125

VIII

List of Figures

Figure 2 1 Stick diagram with vertical ground reaction force (vGRF) traceoverlaid for a ) squat jump (SJ), b ) countermovement jump (CMJ) and c ) drop jump (DJ) 20

Figure 2 2 Quantitive measures of total force used by Dowling and Vamos(1993) 24

Figure 2 3 Geometrical configurations of typical segment 48

Figure 2 4 Isometric force-time curve indicating maximal strength, maximal RFD following three types of training program (Newton R U from www innervations com) 61

Figure 3 1 Diagram of experimental set-up 75

Figure 3 2 Diagram for body segments and angle conventions 78

Figure 3 3 Free body diagram for generic body segment 79

Figure 3 4 Measures of rate of force development 82

Figure 4 1 Joint time histories for a representative subject 86

Figure 5 1 Possible relationships between jump height and a mechanicalparameter 125

Figure 5 2 Interaction of variability and slope of relationship between jumpheight (y axis) and a mechanical jump parameter (x axis) 129

IX

Abbreviations

1 RM one repetition maximum

BCOM whole body centre of mass

BCOMsto rise in the BCOM from standing to take-off

BDJ bounce drop jump

BW body weight

CDJ counter drop jump

CMJ countermovement jump

COM centre of mass

CV Coefficient of variability

DJ drop jump

DJ30 drop jump from 30cm platform

DJ50 drop jump 50cm platform

DJ-H drop jump for maximise rebound height

DJ-H/t drop jump for combination of rebound height and minimum duration

FT fast twitch muscle fibres

G b group analysis based on the highest jump of the 15 jumps undertaken

G m group analysis based on the mean value of the 15 jumps undertaken

HAT head-arms-trunk body segment

JR joint reversal

MV peak angular velocity

RFD rate of force development

ROM range of motion

RPD rate of joint power development

SD standard deviation

SJ squat jump

SSC stretch-shorten cycle

ST slow twitch muscle fibres

TO take-off

vGRF vertical ground reaction force

VJP vertical jump performance

X

The use of intra-subject variability as a means of identifying performance enhancement interventions - Gary F Park

Background The most common method used to identify performance determining biomechanical factors has been to compare differences between individuals This group analysis approach assumes that the movement strategy for all individuals is the same However, not every athlete has the same neuromuscular capacity, anthropometries and muscle morphology It may be more appropriate to make inferences about an individual’s movement strategy by treating each individual as their own experiment group, examining differences between repetitions of an individual’s own performance, referred to as individual analysis The aim of the study is to identify the performance determining biomechanical factors of countermovement vertical jumping, at both a group level and individual level and to highlight the commonality and differences between the two approaches The study also aims to determine whether drop jumps (DJs) overload the performance driving kinetic factors of the countermovement jump (CMJ), thereby assessing the appropriateness of DJs as a training method

Experiment Eighteen male university students performed 15 countermovement jumps (CMJ), 15 drop jumps from 0 30m (DJ30) and 15 from 0 50m (DJ50) From ground reaction force and motion data, kinematic, kinetic and coordination parameters were calculated for the whole body, hip, knee and ankle Correlation analysis was used to identify the biomechanical factors that may explain differences in jump height achieved, both between individuals (inter-subject) and within repetitions of an individual (intra-subject) Differences in kinetic factors between the CMJ, the DJ30 and the DJ50 at a group level was assessed using a two-way repeated measures ANOVA, and at an individual level using a single subject repeated measures ANOVA

Results A number of biomechanical factors were found to be significantly correlated with CMJ height at a group level These however, were not always correlated at the individual level, and visa versa Opposing relationships were evident at the individual level, both between individuals and compared to the group analysis Knee kinetic parameters were significantly greater in the DJ than the CMJ at a group level and for the majority of subjects at an individual level In contrast, both ankle and hip kinetics were not overloaded in the DJ at the group level, although an overload of ankle kinetic parameters was achieved by a number of individuals

Conclusion Results from a group and individual analysis are not always comparable A considerable amount of important information may be lost regarding individual performance strategies when only a group analysis is employed However, the use of solely an individual analysis based approach would not reveal any performance factors relating to differences between subjects, and a case for a group based analysis to be used to supplement an individual analysis therefore exist Knee kinetic factors were overloaded in the DJ compared to the CMJ, while hip kinetics factors were not and the overload of ankle kinetic factors was found to be dependent on the DJ technique employed

Key words vertical jump performance, countermovement jump, drop jump, mtra- subject variability, individualised technique, rate of force development

X I

Introduction

1

1 1 Rational

Endeavours to continually improve an athlete’s performance rely on structured,

progressive training programs, encompassing enhancement of both movement

technique and neuromuscular output capacity Athletes and coaches seek to

determine which factors determine performance success and which training exercise

protocols can be utilised to develop these factors Methods of identifying

performance driving or performance limiting factors have predominantly focused on

group based analyse, either citing the performance strategy of elite athletes as the

‘gold standard’ to which individuals should aspire (Hay, 1995), or identifying

differences between individuals (Dowling and Vamos, 1993) This de-emphasises the

importance of the individual and pertains to an “abstract” or “average” optimal

movement strategy that can be applied to all individuals (Dufek et al, 1995)

However, not every individual has the same neuromuscular capacity (e g individual

joint power, rate of power production and joint dominance), anthropometries (e g

limb length and relative mass) and muscle morphology (e g percentage muscle fibre

type) The unique physical characteristics of individuals, coupled with the multi­

functional degrees of freedom associated with the human body, means that there are a

large number of possible movement strategies Dufek and Zhang (1996) found a

model formulated to explain forces upon landing from a jump, using the group

approach, was suitable for some individuals but not for all This approach would be

valid if everyone was identical Therefore, it may be inappropriate to assume one

optimal movement strategy to be suitable for all It may be more appropriate to

identify an optimum performance strategy for an individual based on differences

between repetitions of the individual’s own performance If this principle is accepted,

it follows that the individual should be the focus of examinations While this may not

be appropriate for all individuals, it may be for elite level performers where minor

refinements of technique are sought and any deviation between what is required to

increase performance for the individual and what was required for the group as a

whole might be unacceptable (Bates, 1996, Hopkins, 1985) By studying each

individual separately, the differences in physical characteristics are controlled and any

change in performance must be due to the movement strategy employed A second

problem with a group based analysis is that, if different movement strategies exist

2

between individuals, it is possible that they may numerically cancel out each other at

the group level, resulting in neither strategies being identified as important

In the present study the CMJ was selected as a model to examine and compare group

and individual based biomechanical analysis This was because it is a relatively

simple and well-learnt task where performance is clearly and objectively defined In

addition, it is evident in many sporting activities The existence of individual

performance strategies in vertical jumping is evident in the literature (Aragon-Vargas

and Gross, 1997b, Hubley & Wells, 1983, Jensen et al, 1991), but only one study

compared the results of both a group and individual analysis (Aragon-Vargas and

Gross, 1997a, 1997b) This study used multiple regression as the statistical method to

identify factors related to vertical jump performance When the sole objective is the

formulation of a model for prediction, multiple regression is suitable However, with

multiple regression the potential exists of the exclusion of relevant variables or

inclusion of an erroneous relationship between a variable and jump height Therefore,

multiple regression may not be the best approach for the identification of

biomechanical parameters that determine jump height and the results of studies using

multiple regression must be viewed with caution Instead, the present study used

bivariate correlation analysis to examine the relationship between each parameter and

jump height

The height achieved in vertical jumping is not simply dependant on the movement

technique employed but also the neuromuscular system’s capacity to produce force

(Tomioka et al, 2001, Walshe et al, 1998) The neuromuscular output capacity is

improved through a progressive overload, using actions that conform well with the

target movement in respect to the muscle groups used, the coordination pattern, the

joint range of motion (ROM), the velocity of contraction and the muscle action

employed (Bobbert, 1990) One such training intervention, which has been

extensively employed, purportedly providing effective overload, is the drop jump

(DJ) However, there are contrasting findings from studies regarding the extent, if

any, of an enhancement in the CMJ following DJ training programs (Blatter and

Noble, 1979, Brown et al, 1986, Matavuji et al, 2001) This may be due to

differences between individuals’ technique For some individuals the joint kinetics

may be overloaded in the DJ compared to the CMJ, while in others no change or a

3

reduction in joint kinetics may be evident Additionally, the kinetic parameters that

are overloaded in the DJ may not be kinetic parameters that require to be trained for

improvements in jump height To date no study appears to have determined if drop

jumps overloads the factors related to CMJ performance at an individual level

Therefore the aims of the present study were to -

(1 ) Identify the biomechanical factors that correlate with jump performance, at

both a group and an individual level

(n) To identify the kinetic factors that are overloaded in the DJ, at both the

group and the individual level

(1 1 1 ) To assess whether the biomechanical (kinetic) factors correlated with jump

height in the CMJ are overloaded in the DJ

(iv) To determine if the kinetic parameters are overloaded more in the DJ50

than the DJ30

(v) To examine the extent to which the results of a group and an individual

analysis are comparable, both for factors that correlate with jump height

and differences in jump conditions

12 Hypothesis

The biomechanical factors that relate to differences in CMJ height at an individual

level of analysis do not always match those at a group level of analysis

A number of joint kinetic parameters are greater in the DJ than the CMJ at both the

group level and the individual level of analysis

A number of joint kinetic parameters are greater in the DJ50 than the DJ30 at both the

group level and the individual level of analysis

The performance determining (kinetic) factors of the CMJ are overloaded in the DJ

4

1 3 Limitations

Correlation measures the extent to which two parameters vary in relation to each

other It does not signify that the change in one parameter causes the change in the

other The precise relationship must be established through systematically altering the

biomechanical parameter while monitoring changes in the jump height achieved

However, for the purposes of discussion in the present study, the theoretical

implications of a causal relationship, which mirrors the findings of the correlation

analysis, will be additionally discussed Bivanate correlation analysis only reveals

linear patterns, the possibility exists that a non-1 inear pattern may be present Visual

examination of scatter plots of each variable and jump height was undertaken Where

a non-linear pattern was suspected, the residuals were plotted against the expected

values from bivariate regression analysis, and the pattern was examined

(Montgomery, 1991) No non-linear patterns were observed for any variable

Limited instruction was given m regards to jump technique during the course of the

experiment, so as not to influence the strategy employed The movement technique

employed in the DJ has been shown to influence the overload of joint kinetics

compared to the CMJ (Bobbert et al, 1987a) Further instruction may have enabled

great overload of joint kinetics, however, it was the response relating to the freely

chosen movement strategy that was of interest

5

Review of Literature

2 0 Introduction

In all facets of human movement no two attempts of the same movement action result

in exactly the same movement kinematics, kinetics or performance outcome

Performance outcomes lie somewhere on a continuous spectrum from worst

performance to best, it is the essence of sports performance to strive for the later

Endeavours to continually reach and surpass the athlete’s best performance rely on

structured, progressive, training programs encompassing enhancement of both

neuromuscular output capacity and movement technique Identification of which

aspect of technique should be trained to enhance performance has traditionally been

based on identifying differences between individuals (Dowling and Vamos, 1993),

often using_performances of elite athletes as the ‘gold standard’ to which individuals

should aspire (Hay, 1995) However, individuals differ m their neuromuscular

capacity (e g individual joint power, rate of power production and joint dominance)

their anthropometries (e g limb length and relative mass) and their muscle

morphology (e g percentage muscle fibre type) Therefore, it may be inappropriate to

expect one technique to be suitable for all and it may be more appropriate to tailor

training programs based on differences between repetitions of an individual’s own

performance Similarly, in attempting to improve a specific neuromuscular

component (e g knee joint power), differences may exist between individuals as to

the extent the component is overloaded when different exercises are employed (e g

drop jump from 30cm vs weighted vertical jumps vs drop jump from 60cm) Again

it may not be appropriate to expect one training exercise to be suitable for all

This review will examine how variability has been viewed in biomechanical and

motor control literature and the role it plays in optimising movement strategy from a

dynamic systems approach The case for a single subject analysis approach will be

put forward and the observed magnitudes of both inter- and intra- subject variability

in the biomechanical literature will be outlined The use and misuse of variability in

biomechanical studies to reveal mechanisms of performance enhancement will be

briefly highlighted, with particular reference to multiple regression analysis

The vertical jump is evident in many sporting activities and has been used as a

research model in numerous biomechanical studies (Bobbert et al, 1987a, Jensen and

7

Phillips, 1991, van Ingen Schenau et al, 1987) due to it being a relatively simple and

well learnt task, where maximum performance is clearly and objectively defined

(Aragon-Vargas and Gross, 1997a) Vertical jumping outcome (i e jump height), is

the combined result of the magnitude of mechanical output of the neuromuscular

system and the coordination pattern (technique) employed This review will outline

the biomechanical variables that have been examined in the study of vertical jumping

and their relationship to jump height, along with a review of studies that have sought

to investigate the coordination pattern employed

Finally, training methods employed to improve vertical jump performance will be

examined, with a particular emphasis on drop jumping (DJ) How changes in the DJ

technique or drop height can affect the magnitude of kinetic parameters will be

examined Finally, a brief outline of results of training studies utilising the DJ will be

detailed

2 1 Variability

This section will introduce the idea of variance and will briefly outline the various

theories of movement control, which have been forwarded in the motor control

literature The case will be put forward for viewing the control of the human body as

a dynamic system and examine the role variability plays in shaping movement pattern

formation The amount of variability observed in the biomechanical analysis of a

variety of movements will be given, both between subjects (inter-subject) and within

repeated performances by an individual (intra-subject) Statistical methods, which

utilise variance as a means of identifying trends in the data, will be briefly evaluated,

outlining their merits and limitations

2 11 Variability in movement

Several attempts to solve the same motor task will inevitably lead to different patterns

of movement actions, including kinematic, kinetic, muscle activation (Latash et al,

2002) and movement outcome Bernstein (1967) referred to this as ‘repetition

without repetition’, meaning each repetition involves a unique, nonrepetitive

movement pattern (Latash et al, 2002) This tendency for repetitions to differ from

8

each other is referred to as variability (Orr, 1995) and is a natural occurring

phenomenon associated with all types of human movement (DeVita & Bates, 1988)

Variability within an individual’s performances is referred to as intra-subject

variability (Aragon-Vargas & Gross, 1997a & b, DeVita & Skelly, 1990) or within-

subject variability (Borzelli et al, 1999, Heiderscheit, 2000), while variability between

individuals is referred to as inter-subject variability (Aragon-Vargas & Gross, 1997a

& b, Borzelli et al, 1999) or between-subject variability (Hopkins et al, 1999) In

spite of the widespread evidence of variability in movement, it has not been given the

same theoretical and operational significance that invariance has procured, based on

the belief that consistency of response is indicative of a motor strategy

2 12 Movement control theories

Some theories of motor control have long proposed that movement is controlled by

centrally stored patterns (or prescriptions), which function with little or no sensory

input during completion of the task (Gentner, 1987) This suggests that for each

possible movement-environment combination a separate motor program must exist

However, this would lead to immense memory storage requirements In

acknowledgement of this limitation, Schmidt (1975) forwarded the notion of a

generalised motor program for a given class of movement, rather than each specific

movement These generalised motor programs present pre-structured commands for a

number of movements, which can be adjusted for velocity and force requirements

when specific response parameters are provided (Schmidt, 1975) Relative timing

invariance in the kinematics of movement has been cited as evidence to support the

generalised motor program theory (Schmidt, 1985) However, a number of authors

have clearly shown that timing invariance is not apparent in many movements

(Burgess-Limerick et al, 1992, Genter, 1987, Maraj et al, 1993) and the procedures

used previously to support the general motor program were inappropriately applied

(Gentner, 1987)

Over the last three decades there has been substantial work by ecological

psychologists rejecting the idea of invariance in favour of a the concept of functional

variability The introduction of concepts and methods of nonlinear dynamics and

chaos theory has led to the interpretation of movement variability as more than merely

9

noise but as being necessary for movement pattern optimisation and driven by a

deterministic process It has been suggested that the problem of movement pattern

selection and production can be resolved by conceptualising the human movement

system as a complex dynamic system (Clark et al, 1989, Diedrich and Warren, 1995,

Newell and Slifkin, 1998, Stergiou et al, 2001) Complex systems such as the human

body exhibit many fundamental attributes, including many degrees of freedom which

are free to vary, many different interacting levels of the system (neural, perceptual

and muscular-skeletal), non-linear output and the capacity for stable and unstable

patterns as it spontaneously shifts between coordination states through processes of

self-orgamsation (David et al, 2000)

Complex systems are seen as open non-conservative systems with variable amounts

of kinetic energy dissipated around its components at any given moment The energy

already in the system interacts with instantaneously available forces in the

environment, such as reactive forces and gravity The energy entering the system can

interact with energy already within the system to produce chaotic and unpredictable

effects on the system However, there appears to be a surprising amount of stability

within the systems, suggesting that processes of self-organisation are present which

maintain the stability

From a dynamic systems viewpoint, movement pattern formation is the result of the

self-organisation of the neuromusculoskeletal system confronted with the specific

dynamic constraints of the task and environment, as opposed to spatio-temporal

prescriptions from a hierarchical control system (Temprado et al, 1997) Variability

in the system should not be considered merely as noise but predominantly as a

functional property, which allows the system to explore new movement patterns

From this perspective variability can be viewed as an index of fluctuation necessary to

allow the movement system to adapt to changing constraints from one situation to the

next (Button et al, 2003) Given the functional nature of variability, higher levels of

variability m certain parameters may be indicative of a highly skilled adaptation to

task constraints, rather than merely a reflection of motor system noise (Davids et al,

2000) Clearly, since variability may be the result of the system exploring new

movement patterns, variability may provide a window for the identification of

optimum movement patterns

10

2 13 Variability in Biomechanics studies

Variability, both inter-subject and intra-subject, is evident in all movements Tables

2 1 to 2 6 detail examples of both inter-subject and intra-subject variability reported

for biomechanical parameters for gross motor tasks Table 2 1 and table 2 2 report

magnitudes of variability experienced in a variety of movements, while tables 2 3 to

table 2 6 specifically detail jumping tasks Table 2 1 examines the initial impact peak

forces for a variety of landing actions The ratio of intra-subject variability to mter-

subject variability ranges from approximately half (Dufek et al, 1995) to comparable

magnitudes (Dufek and Bates, 1990, Lees and Bouracier, 1994)

Table 2 1 Coefficient of variance (CV) [%] of initial impact forces in selective landing actions__________ _ _ _________Study Inter Intra Intra

Mean RangeRunning

Stergiou et al (2001) 126Lees & Bouracier (1994) 9 1 93 5 5 - 14 1Miller (1990) 12 1Dufek et al (1995) 20 9 88 6 3 -1 0 5

WalkingHam ill & McNiven (1990) 5 3Hamill et al (1984) 93

Landing from vertical drop (60cm)Dufek & Bates ( 1990) 143 29 1 23 6 -3 3 1Dufek & Bates ( 1991 ) 25 9Dufek et al (1995) 26 9 140 8 31 -2 3 2

A considerable amount of variability exists in the kinetics of movement both inter-

subject and intra-subject Lees and Bouracier (1994) found the average intra-subject

coefficient of variability (CV) for vertical impact force to be approximately the same

magnitude as the inter-subject CV However, individual levels of intra-subject CV

ranged from 60 4% to 154 9 % of the inter-subject CV observed At a segmental

level, DeVita and Skelly (1990) found the intra-subject CV for joint moments to be

58%, 44% and 47% of the inter-subject variation for hip, knee and joint moments,

respectively, during the support phase of running

11

Table 2 2 CV [%] of stride length during running at various running velocitiesStudy 2 5m/s 3m/s 3 5m/s

Inter 4 6 45 12 2Craib et al (1994) Intra 25 22 23

1 3-3 3 1 7-3 3 1 2-4 3Cavanagh & Kram (1989) Inter 57 5 9Heiderscheit et al (2002) Inter 6 1Schieb (1986) InterNote Velocities have been reported to nearest 0 5m/sAverage and range of individuals intra-subject variability is outlined for Craib et al (1994)

Table 2 2 shows the magnitude of inter-subject variability in stride length during

running at selected velocities Intra-subject variability is also detailed for Craib et al

(1994), where similar percentages of intra-subject CV to inter-subject CV of stride

length for running velocities of 2 7m/s and 3 1 m/s were found (54% and 49%

respectively) At a higher velocity of 3 5m/s the intra-subject CV was relatively

smaller compared with inter-subject CV This can be attributed to a greater range of

stride lengths chosen by individuals at the higher velocity, thus increasing mter-

subject variance Since the individual CV of stride length did not significantly differ

across velocities, the reduction in the percentage can be attributed to a change in inter-

subject variance alone No data for intra-subject variability was reported for the other

studies

Table 2 3 outlines the inter-subject CV for vertical jump height achieved in the

countermovement jump (CMJ) Additionally, intra-subject data for Aragon-Vargas &

Gross (1997b) is reported, which is of a reduced magnitude compared to inter-subject

variability

Table 2 3 Inter-subject and intra-subject standard deviation [m] and CV[%] for height attained in the CMJ

Study number of variance SD CV__________________subjects type_______

Aragon-Vargas & Gross (1997a) 52 Inter 0 070 13 4Aragon-Vargas & Gross (1997b) 50 trials Intra 0013 3 1Dowling & Vamos (1993) 97 Inter 0 101 34 0Jaric et al (1989) 39 Inter 0 050 132Robertson & Fleming (1987) 6 Inter 0 850 170Rodacki et al (2001) 20 Inter 0 044 13 2Nagano et al (1998) 6 Inter 0018 52Van Soest et al (1985) 10 Inter 0 060 11 1

12

Variability in the duration of the concentric phase in the CMJ is shown in table 2 4 as

an example of temporal variability for a jumping task Only one study could be found

that detailed both inter- and intra-subject variability (Aragon-Vargas & Gross, 1997a,

1997b) As with the height attained in the CMJ outlined in table 2 3, inter-subject

variability is greater than intra-subject variability

Study Inter Mean Intra Range IntraAragon-Vargas & Gross (1997) 196 6 4 5 6-6 8Jaric et al (1989) 192Rodacki et al (2001) 144Van Soest et al (1985) 15 85

Table 2 5 details inter-subject variability observed in a single study by Van Soest et al

(1985) for joint kinematic and kinetic parameters in the CMJ Comparisons can be

made across variables as each was produced from the sample group Lower

variability was observed for the joint angle data (kinematic measure) than moment,

power and work data (kinetic measure) There does not appear to be a difference

between the joints in terms of the magnitude of variability This is supported in

general, in analysis of joint moment and power data for the CMJ (table 2 6)

Table 2 5 Inter-subject CV[%] of segmental data for the CMJ (van Soest et al, 1985)Hip Knee Ankle

Angle @ JR 16 13 17 39 991Peak Moment 16 25 18 39 16 90Peak Power 23 47 21 06 26 53% Work 18 23 22 02 24 15Note JR = joint reversal (point where angular motion of the joint reverses

Table 2 6 Inter-subject CV [%] for joint moment and power in the CMJStudy Joint Peak moment Peak Power

Hip 25 1 28 4Aragon-Vargas & Gross Knee 35 1 30 1(1997a) Ankle 197 29 1

Hip 11 5 14 2Ravn et al (1999) Knee 70 9 1

Ankle 183 20 8Hip 21 3 28 3

Rodano & Roberto (2002) Knee 20 0 23 7Ankle 14 2 15 8Hip 163 23 5

Van Soest at al (1985) Knee 184 21 1Ankle 16 9 26 5

13

2 14 The use of variability in movement assessment

Human movement performance is dependent on the interaction of numerous

biomechanical factors Vertical jump height is predominately determined by the

vertical velocity of the body’s centre of mass (BCOM) at take-off Whole body

vertical velocity in vertical jumping is in part a function of individual joint angular

velocities, which in turn are in part dependent on individual joint kinetics Joint

kinetics has been seen to vary both between individuals and within repetitions by an

individual for vertical jumping (Rodano and Roberto, 2002, Van Soest et al, 1985)

Likewise, variability has been observed in performance outcome (table 2 3) As the

performance outcome is dependent on a number of biomechanical factors, it seems

intuitive to assume the variability in performance outcome may be the result of

variability in these underlying joint kinematics and kinetics, and knowledge of how

they vary in relation to each other may provide a means of identifying differences in

performance

Variance has normally been viewed as a nuisance, requiring additional measurements

to obtain a representative value and the use of statistical inference to determine

differences However, variance may reveal information about the movement pattern

and can be used as a means of analysis Variance with respect to the interrelationship

among variables is called covariance and examines the extent to which two sets of

variables exhibit similar tendencies to differ (Orr, 1995) Two statistical methods that

are based on covariance are correlation and regression

Correlation was first put forward by Galton in 1888 in his paper to The Royal Society

of London, referring to it as an “index of co-relation” (Stigler, 1986) Correlation

measures the extent to which the variance of one parameter can be explained by the

variance of another

An extension of correlation is bivariate linear regression, which involves producing

the equation of a line that passes through the data plotted on a Cartesian plane such

that the squared deviation of the observed points about the line are minimised

Bivariate regression can be simply viewed as a line that best represents the trend in

the data However, as the number of parameters increase it becomes difficult to

14

visualise the model of best fit for the data, but formulation of a mathematical model of

the relationship is still possible via multiple regression and has been used in a number

of biomechanical studies (Aragon-Vargas and Gross, 1997a, Dowling and Vamos,

1993, Dufek et al, 1995, Hay et al, 1978, Tomioka et al, 2001) Multiple regression

always explains at least as much variability in the dependant variable as bivariate

regression, but the potential of a sample specific relationships increases with the

number of variables that are included in the model Clearly it would be beneficial to

have a method to reduce the number of variables entering the model The most

commonly employed method of variable elimination in biomechanical studies is by

stepwise regression (Aragon-Vargas & Gross, 1997a, Dufek et al, 1995, Hay et al,

1978) This can take the form of backwards or forward elimination, resulting in eithert

variables being removed from a model containing all the variables or variables being

added to the bivariate model containing the variable most strongly correlated with the

dependent variable

Aragon-Vargas and Gross (1997a) used multiple regression to identify the

biomechanical factors that distinguish differences in jump height between 52

individuals The three regression models that explained the largest amount of

variance in jump height along with the best single variable predictor at both a whole

body and segmental level were reported In a subsequent study they examined the

biomechanical factors that determined jump height within individuals and selected

three subjects to represent the best, worst and average performers (subject B, subject

W and subject A, respectively) Factors contained within the regression models of at

least two of the three subjects were tested to determine it they significantly related to

jump height for a further five subjects

Even though the model obtained with multiple regression may be the best possible for

prediction, stepwise regression is pure empirical selection and may not include all

theoretically relevant variables One of the biggest problems involved in multiple

regression is the predictor variables being correlated with each other, which is

referred to as multicollinearity (Grimm & Yamold, 1995) When multicollinearity is

present, variables strongly correlated with each other may not be included together

because when one of the variables is already in the model, the inclusion of the other

may contribute only a diminished source of explained variance in the dependant

15

variable This may increase the likelihood of inclusion of variables primarily as the

result of being uncorrelated with the existing variables in the model and at the

expense of variables more strongly related to the dependant variable This was

highlighted in the study of vertical jumping by Aragon-Vargas and Gross (1997a)

where the amplitude of the BCOM was the best single predictor of jump height for

subject A (r = 0 557) but was not included with other variables in the best three

multiple regression model

A greater problem occurs when two variables, highly negatively correlated with each

other, are included in a regression model together This may result in the coefficient

of one variable changing sign to accommodate the other within the model (Hair et al,

1987), thus predicting the opposite relationship the parameter has with the dependant

variable This occurred in the group regression models explaining the variation in

jump height in Aragon-Vargas and Gross (1997a) Both peak hip moment and hip

moment at the point where the joint reverses direction, termed joint reversal (JR),

were positively correlated with jump height on their own (r = 0 524 and r = 0 484,

respectively), but when included with other variables (models 16 and 17, p36)

displayed a negative relationship within the model While this does not cause a

problem when the model is used for purely prediction but misleading information may

be drawn about the individual relationship a variable has with jump height

Multiple regression analysis is suitable if the sole objective is the formulation of a

model for prediction, but when used to gam insight into the effect of various

parameters on a dependant variable, monitoring of multicollinearity is critical Of the

biomechanical studies mentioned above, only Dufek et al (1995) and Tomioka et al

(2001) investigated whether the variables entered into the stepwise process were

uncorrelated Aragon-Vargas & Gross (1997a, 1997b) and Dowling and Vamos

(1993) in their analysis of vertical jump performance entered a multitude of

biomechanical parameters into the stepwise process with no stated consideration

given to whether the variables were correlated or uncorrelated In light of the inter­

related nature of the human movement system, the assumption of uncorrelated

predictor variables is highly likely to have been violated

Aragon-Vargas and Gross (1997a) stated “the purpose of this study was to identify the

relevant predictors and not necessarily to build the most accurate model” (p32), after

16

previously stating, “since most factors proposed as relevant to VJP (vertical jump

performance) are interrelated in a complex fashion, a sensible approach to their study

is the use of a multiple-regression analysis technique” (p26) In light of their aim,

instead of rejecting multiple regression due to the potential effects posed by

multicollinearity, which they acknowledge may be present, they utilised a technique

that has the potential for excluding relevant variables from the model This was

illustrated by only including the ankle and hip angle at take-off in one model,

explaining differences in the vertical height difference of the BCOM between

standing and take-off, and the knee angle being included in another model Multiple

regression does not allow for the fact that potentially a relevant predictor may not be

included in any model due to the inclusion of another factor, nor does it protect

against the reversal of the sign of the relationship as highlighted above with respect to

peak hip moment and hip moment at JR This makes multiple regression an

unsuitable means of identifying relevant factors of jump performance Findings from

studies, which use multiple regression with no reference to the degree that predictor

variables are correlated, must be viewed with caution

To avoid multicollinearity, the selection of variables that measure the same (or

similar) factors must be eliminated To reduce the effect of multicollinearity a

number of approaches may be employed including transformation of the data or the

use of techniques such as factor analysis (e g principle component analysis) Factor

analysis combines individual parameters into new uncorrelated parameters, which can

be subsequently used in regression techniques (Freund & Minton, 1979) These new

parameters, called factors, form linear combinations of the original parameters

Kollias et al (2001) used principle component analysis to investigate the effect of

changes in strength and coordination m vertical jumping but did not relate the new

factors to changes in performance While satisfying the conditions of regression

techniques, these new factors introduce complications in interpretation of the results,

as often no meaningful combinations are produced

One way of protecting against these potential pit-falls of multicollinearity, while still

gaining insight into the mechanics of performance enhancement, is to examine the

relationship between each parameter and changes in the performance outcome

individually by means of bivariate correlation analysis This approach has been used

17

in a number of biomechanical studies (Dowling and Vamos, 1993, Harman et al,

1990, Jane etal, 1989)

4 15 Group analysis verses individual subject analysis

The group approach to technique analysis presumes that a single, ‘abstract’ optimal

movement strategy exists and it can be applied to all individuals This would be true if

everyone was physically identical However, individuals differ in their neuromuscular

capacity (e g individual joint power, rate of power production and joint dominance)

their anthropometries (e g limb length and relative mass) and their muscle

morphology (e g percentage muscle fibre type, angle of muscle pennation) The

unique physical characteristics of individuals, coupled with the multi-functional

degrees of freedom associated with the human body, allow the possibility of diverse

movement strategies to exist A strategy is a neuromusculoskeletal solution for a

given performance task, resulting in a unique pattern of movement and variability due

to biomechanical, morphological and environmental constraints (Bates, 1996)

Evidence of individual strategies is abundant in the literature for jumping (Aragon-

Vargas and Gross, 1997b, Jensen and Phillips, 1991, Rodacki et al, 2002), landing

(Lees, 1981, Dufek and Bates, 1991, Dufek and Zhang, 1996, Dufek et al, 1995) and

running (Dufek et al, 1995, Lees and Bouracier, 1994)

Dufek and Bates (1991) assessed the impact properties of four types of sports and

found the impact forces across subjects did not follow a consistent trend for all shoe

conditions While one shoe was determined as the best for the group the same shoe

was not best for all individuals within the group Lees (1981) also found variation in

landing pattern between subjects and analysed in detail the two extreme cases, hard

and soft landings Dufek et al (1995) also found different landing strategies for

individuals Lees and Bouracier (1994) while investigating the shock absorbing

characteristics of individuals during running found differences in the braking force

between experienced and non-experienced runners Such changes in shock absorbing

strategies would potentially obscure the effect of an intervention investigating

footwear Jensen and Phillips (1991) in their study of coordination of jumping

activity found no constant pattern of joint reversal for all subjects While hip-knee

sequencing was stable across jumps for all subjects, only two of the six subjects

18

maintained the sequence of extension between the ankle and knee joint Changes in

the pattern of joint reversal between individuals were also observed by Aragon-

Vargas and Gross (1997a) and Rodacki et al (2002)

Dufek et al (1995) found that a single mechanical parameter explained variance in

both the first and second impact peak experiences during landing at a group level

However, only two of the six subjects used the same landing strategy as the group

model for the first impact peak and none of the individuals used the group strategy for

the second impact peak During running Dufek et al (1995) found none of the six

individuals performed like the group average, where a single knee variable explained

the variance in the impact peak, instead three distinct strategies of shock attenuation

were observed at the individual level, none of which included the group predictor

They concluded that the group approach produced a mythical “average” performer,

which did little to explain the performance strategies for individual subjects

Aragon-Vargas and Gross (1997a) used multiple regression to identify the

biomechanical parameters at both the whole body and joint level that distinguished

differences in jump height between 52 individuals and between repetitions of an

individuals own movement (Aragon-Vargas and Gross, 1997b) The best whole body

predictors of jump height at a group level (peak and average power), were also

significant predictors for all individuals examined Amplitude of movement, while

present in the prediction models at a group level, was not significant for six of the

eight individuals examined At the group level, peak hip power was the best

segmental predictor of jump height but at an individual level was only a significant

predictor for six of the eight subjects Additionally, while ankle joint kinetics

appeared in numerous models of jump height at an individual level, no ankle kinetic

parameters appeared in the models at the group level

19

2 2 Biomechamcs of vertical jumping

Numerous biomechanical variables have been examined at the whole body and

segmental level in an effort to gain insight into factors that determine vertical jump

performance The magnitude of the biomechanical variables and where possible their

relationship with jump height observed in these studies are outlined in this section

&

Figure 2 1 Stick diagram with vertical ground reaction force (vGRF) trace overlaid for a ) squat jump (SJ), b ) countermovement jump (CMJ) and c ) drop jump (DJ) (Voigt et al, 1995)

Three types of vertical jump have commonly been used in biomechamcal studies, the

squat jump (SJ), the countermovement jump (CMJ) and the drop jump (DJ) In the

squat jump (SJ) the subject starts from a stationary, semi-squatted position with knees

and hip flexed for a few seconds, before vigorously extending causing the BCOM to

rise vertically When subjects are asked to jump for maximum height, predominately

a countermovement is spontaneously employed (Bobbert, 1990) The

countermovement jump (CMJ) starts with the subject in an erect position from which

they lower their BCOM quickly, before vigorously rising again as the joints are

extended In the DJ increasing the initial height that the BCOM is held above that of

standing increases the amount of negative work further The body dropping under the

20

force of gravity starts the DJ and upon landing, a jump for maximum height is

performed Drop jumping will be discussed in section 2 4, while section 2 2 and 2 3

will focus primarily on the mechanics of the CMJ

2 2 1 Vertical jump mechanics

Jumping for height is a skill involved in many sporting activities and dance Most

healthy individuals can jump and a capacity for jumping is evident from an early age

(Clark et al, 1989) Differences in height achieved during jumping are evident both

between individuals and within repeated jumps by an individual Numerous possible

movement strategies exist and knowledge of which strategy yields the greatest jump

height would be of benefit to coaches and athletes in order to guide training programs

to maximise jump height Once knowledge of the mechanisms that enhance jump

performance is gained, more informed and specific training interventions could be

formulated

The aim of vertical jumping is to raise the BCOM as high as possible above the

ground This is achieved by exerting a vertical force greater than the weight of the

body against the ground by means of the neuromuscular system However, the human

body is a multi-task machine, capable of performing many diverse movements and is

not only designed to project the body vertically Due to this multi-functionality, the

muscles’ line of action are not oriented specifically to exert a force directly

downwards, thus the body must reorganise itself though a well coordinated series of

carefully timed rotations of the various body segments to exert a collective force

downwards To achieve this, the body must take into consideration the anatomical

constraints the structure of the body imposes in light of additional constraints related

to the task

Jump height is determined by vertical velocity of the BCOM at take-off and it’s

vertical position above the ground at take-off (Dowling & Vamos, 1993, Hay et al,

1978) The relative contribution of the rise of the BCOM above standing height at

take-off has been found to be between 25% (Bobbert et al, 1996) and 29% (Hannan et

al, 1990) of the total height achieved The vertical velocity of the BCOM, is

determined by the vertical impulse exerted in excess of that needed to support the

21

mass of the body The vertical impulse in turn is sum of the angular impulses exerted

by the individual joints (Hay et al, 1979) The angular impulse is the product of the

average joint moment during the propulsion phase and the time of movement To

gain insight into the factors affecting jump height achievement, not only do the forces

and velocity acting on the whole body before take-off need to be examined, but also

examination of individual joints is required

2 2 2 Whole body kinematics

The amplitude of movement of the BCOM is the distance over which the BCOM

travels during the concentric phase The greater the movement amplitude of the

BCOM, the further the distance over which the body can exert a force and the greater

the potential take-off velocity The amplitude the BCOM moves during the

concentric phase has been examined in numerous studies (Aragon-Vargas and Gross,

1997a, Bobbert et al, 1986a, Bobbert et al, 1987a, Bobbert et al, 1996, Nagano et al,

1998, Rodacki et al, 2001) These studies have been in close agreement, reporting

that the amplitude the BCOM travels of approximately 0 35m However, Nagano et al

(1998) and Rodacki et al (2001) found greater amplitudes of 0 49m and 0 48m,

respectively Only one of these vertical jumping studies examined how different

amplitudes affected the jump height achieved Aragon-Vargas and Gross (1997a)

used multiple regression techniques to identify relevant predictors of jump height and

found almost all models included this amplitude moves as a predictor of jump height

Vertical jumping is a ballistic movement taking less than a second to perform (Bedi et

al, 1987, Bobbert et al, 1987a, Rodacki et al, 2001) A greater amount of time is

spent during the vertical deceleration of the body (eccentric phase) than the

propulsion (concentric phase) The eccentric phase lasts on average between 0 45s

(Bosco and Komi, 1979) and 0 72s (Rodacki et al, 2001), while the concentric phase

lasts on average between 0 2s and 0 3s (Bedi et al, 1987, Bobbert et al, 1987a, Jane et

al, 1989) (table 2 6)

22

Table 2 7 Duration of the eccentric and concentric phases of the CMJ

StudyNumber of subjects

Eccentricphase(seconds)

Concentricphase(seconds)

Total

(seconds)Aragon-Vargas and Gross (1997) 52 na 0 32 naBedi et al (1987) 32 0 64 0 20 0 84Bobbert et al (1987a) 10 0 55 0 29 0 84Bobbert et al (1996) 6 na 0 33 naBosco & Komi (1979) 34 0 45 0 22 0 67Fukashiro & Komi (1987) 1 na 0 26 naJane et al (1989) 39 0 53 0 26 0 79Rodacki et al (2001) 20 0 71 0 28 0 99

2 2 3 Whole body Kinetics

Through the impulse-momentum relationship vertical impulse, normalised for body

weight, is directly related to vertical velocity at take-off Table 2 7 outlines typical

magnitudes of the average vertical ground reaction force (vGRF) and vertical impulse

reported in the literature Relatively consistent magnitudes of impulse have been

reported, ranging between 280Ns and 380Ns (Bedi et al, 1987, Harman et al, 1990,

Rodacki et al, 2002) The greater impulse observed by Bobbert et al (1987a) is

consistent with the greater jump height and longer concentric phase observed in that

study

Table 2 8 Average whole body vGRF and vertical impulse during concentric phase of the CMJStudy Number of

subjectsAverage Force

N N/kgImpulse

(Ns)Bedi et al (1987) 32 1836 23 6 369Bobbert et al (1987a) 10 1715 20 2 497Bosco & Komi (1979) 34 1017 12 9 naHarman et al (1990) 18 na na 281Rodacki et al (2002) 11 na na 300

Hay et al (1979) examined vertical impulse over eight separate phases of the CMJ and

only found that the vertical impulse during the concentric phase was correlated with

jump height Bosco and Komi (1979) however, found net vertical impulse in both the

eccentric phase (r = 0 62) and concentric phase (r = 0 78) to be correlated with jump

23

height Findings that positive impulse correlates with jump height adds little to the

knowledge of how to enhance jump performance as it is directly related to vertical

velocity at take-off (Impulse-momentum relationship) Dowling and Vamos (1993)

examined the ratio of negative to positive impulse to gain additional insight and found

the ratio to be correlated with jump height (r - -0 514), but impulse in the negative

phase alone was not correlated with jump height and the findings may have purely

reflected a greater positive impulse rather than a factor of mechanical enhancement

The lack of significance for the negative impulse led Dowling and Vamos (1993) to

conclude that the countermovement phase is purely to take up the slack in the muscles

at the onset of the concentric phase and to allow the muscle enough time to reach

maximum activation at the joint angle that allows the greatest moment

Note a) box approximation of total positive force B W body weight

Figure 2 2 Quantitive measures of total force used by Dowling and Vamos (1993)

The force-time curve is a complex function and reveals information such as minimum

and maximum values and the rate of force development (RFD), while the area under

the curve quantifies the total magnitude of force applied (Figure 2 2) To simplify the

force-time relationship many authors have focused on discrete information from the

curve or taken a more simplistic approach to quantify the total magnitude of force

applied To get an indication of the total force applied Bobbert et al (1987a) and

Bosco and Komi (1979) examined the average force during the concentric phase,

while Dowling and Vamos (1993) examined the area contained in a box which

enclosed the force curve (Figure 2 1) A single point estimate measures have also

been used including peak force (Fukashiro and Komi, 1987, Harman et al, 1990,

Robertson and Fleming, 1987), and peak force expressed relevant to body weight

(Bobbert et al, 1987a) Harman et al (1990) and Robertson and Fleming (1987) report

24

values of peak force approximately 2 3 times body weight (BW) A greater average

peak value found by Bobbert et al (1987a) (2 52 BW) is consistent with the greater

impulse observed in that study

Table 2 9 Peak vGRF during vertical jumpingStudy Number of Peak Force Relative peak

subjects (N) force (N/kg)Fukashiro & Komi (1987) 1 2146 29 0Harman et al (1990) 18 1697 22 7Bobbert et al (1987a) 10 2094 24 7

Both peak force (r = 0 519, p< 0 01) and the time from peak to take-off (r = -0 274, p<

0 01) have been found to be significantly correlated with jump height (Dowling and

Vamos, 1993) Achievement of peak acceleration of the BCOM or peak force late in

the movement may be optimal when high end point velocity is required, but this may

require considerably more muscular power and may be limited due to physiological

constraints (Dowling & Vamos, 1993) Although Dowling and Vamos (1993) found

maximum force to be significantly correlated with jump height, some jumps with a

large peak force did not result in a corresponding greater jump height

The rate of isometric force development for the knee joint as measured by greatest

change in force has been found to be related to jump performance (r = 0 825)

(Paasuke et al, 2001) If a poor correlation between maximum force and the rate of

force development exist this would explain why individuals with a high peak force

exhibited poor jump performance Rate of force development will be discussed in

detail in section 2 2 6 Pandy and Zajac (1991) suggested a rapid increase in vertical

force at the start of the concentric phase sustained close to take-off is optimum in

vertical jumping

Since vertical jumping requires both high forces and velocity, it is believed that high

values of power are desirable (power = force x velocity) Power can be seen as the

combination of strength and speed and represents the ability to produce a high level of

work through a given distance (Kerin, 2002) (work = force x distance) Bosco and

Komi (1979) found average power to be a better predictor ofjump height than

average vGRF (r = 0 74 and r = 0 51, respectively) Peak whole body power has been

25

found to be the best mechanical predictor ofjump height explaining between 52% and

86% of the variance in height achieved (Aragon-Vargas and Gross, 1997a, Dowling

and Vamos, 1993, Harman et al, 1990) (r = 0 72, p < 001, r = 0 928, p <0 01 and r =

0 84, p <0 01 respectively) Peak whole body power was also found to be

significantly correlated with jump height at an individual level for the ten subjects

examined by Aragon-Vargas and Gross (1997b) However, these authors did not find

it to be the best predictor ofjump height for the three representative individuals

examined in detail, instead they found that peak negative impulse, amplitude the

BCOM travelled and average power were the best predictor ofjump height for the

three individuals This study (Aragon-Vargas and Gross, 1997b) is the only study to

examine factors that correlate with jump height at an individual subject level, and

clearly indicates that individuals differ in which factors are important for success in

jump height achievement

Given such a strong association between peak power and jump height, surprisingly

peak power has not been evaluated in many jump studies Bosco and Komi (1979)

and Harman et al (1990) are in close agreement reporting peak values of 2984W,

3216W (43 W/kg) and 3260W, respectively, while a higher average peak value of

3863 W (52 W/kg) was reported by Aragon-Vargas and Gross (1997a) In light of the

strong relationship between peak power and jump height, Dowling and Vamos (1993)

suggested that simply increasing strength may not be enough to ensure improvement

in jump performance, but strength should be increased specifically at high velocities

Zajac (1993) examined the influence of muscular strength and speed on vertical squat

jump performance using an optimal control model (mathematical based) They found

that when strength and speed were enhanced independently by 100%, jump height

increased more (120%) from strength enhancement than from speed enhancement

(60%)

Table 2 10 Total work done during the concentric phaseStudy Number of Work done Relative work

subjects (J) done (J/kg)Hubley and Wells (1983) 6 679 85Fukashiro & Komi (1987) 1 658 89Bosco & Komi (1979) 34 656 84

26

Three studies have examined the total amount of work done in the concentric phase

(Bosco and Komi, 1979, Fukashiro and Komi, 1987, Hubley and Wells, 1983) (table

2 10) The greater amount of work done by the subject examined by Fukashiro and

Komi (1987) is consistent with the greater jump height observed compared to Bosco

and Komi (1979) No comparisons can be made with the study by Hubley and Wells

(1983) as no jump performance data is available

While a greater amount of work done can be assumed to increase jump height,

provided the distance over which the body moves remains the same, no studies appear

to have examined this relationship While Aragon-Vargas and Gross (1997a) did not

directly examine the relationship between the amount of work done and jump height,

average whole body power and the duration of the concentric phase appeared in

tandem within their prediction models for jump height The direct relationship

between jump height and work done, both in the eccentric and concentric phase, has

yet to be examined

2 2 4 Segmental kinematics

Segmental kinematics and kinetics are the result of how an individual’s nervous

system uses their neuromuscular capacity to maximise jump height (Aragon-Vargas

and Gross, 1997a) The amplitude the BCOM travels, as discussed earlier, is the

result of the combined effect of an individual joint’s maximum angular displacement,

and determines the distance over which work can be done While numerous studies

have reported the peak joint angle attained in vertical jumping (table 2 11), none of

these have examined the effect changes in peak joint angles have on jump height The

greater the peakjoint angle the further the distance over which work can be done

However, a greater knee angle may not necessarily be optimum Bobbert et al (1996)

found a reduced jump height when a lower position of the BCOM at the start of the

concentric phase was utilised in a SJ compared to a SJ where the height that was

freely chosen in a CMJ was used Factors other than the distance over which to apply

force may be important in the selection of the greater angle the knee joint attains in

the CMJ Thorstensson et al (1976) determined an optimum knee angle exists for

isometric force production, while Bosco et al (1981) found a reduced knee angle

enabled better utilisation of the stretch-shorten cycle (SSC) However, due to

27

differences in anthropometries and neuromuscular capacities between individuals, the

optimum joint configurations at the start of the concentric phase may differ between

individuals, and analysis at an individual level may be more beneficial

Table 2 11 Peak joint angle during vertical jumpStudy Number of

subjectsRadians Degrees

Hip 1 12 64 2Bobbert et al (1996) 6 Knee 1 31 75 1

Ankle 126 72 2Hip 1 23 70 5

Bobbert et al(1987a) 10 Knee 1 40 80 2Ankle 1 23 70 5Hip 1 75 100 0

Jaric et al(l 989) 39 Knee 1 71 98 0Ankle na naHip 1 20 68 6

Rodacki et al (2001) 20 Knee 1 56 89 5Ankle 1 64 94 1

Angular velocities of individual joints act in combination to maximize the vertical

velocity of the BCOM Table 2 12 outlines peak angular velocity of the joints of the

lower extremities during vertical jumping To maximize vertical velocity of the

BCOM it appears that these peak joint angular velocities need to be carefully

coordinated in both sequence and timing, a factor discussed in 2 3 1

Table 2 12 Peak angular velocity of joints during concentric phaseStudy Number of

subjectsRadi an/s Degree/s

Hip 11 1 636Bobbert et al (1987a) 10 Knee 167 956

Ankle 16 1 922Hip 85 487

Rodacki, et al(2001) 20 Knee 12 5 716Ankle 102 584

2 2 5 Segmental kinetics

The force that the whole body exerts against the ground is the sum of the moments at

each joint The net muscle moments about a joint is the sum of moments exerted by

agonists, antagonist and passive structures around the joint such as the joint capsule,

ligaments and tendons (Bobbert and van Ingen Schenau, 1988) It is of limited use to

know that an increase in the total force exerted enhances vertical jump performance

28

Understanding how each joint contributes to this total force provides more significant

information, as it may identify areas of deficiency in jump performance for an

individual and guide future training interventions Investigations into the mechanisms

of jump height achievement have seldom focused on activity at a segmental level

Hay et al (1979) found the average moment for the hip and knee joints during the first

half of the concentric phase were significantly related to jump height (p <0 001), but

the magnitude of the correlations were not reported However, no significant

relationship was observed for the second half of the concentric phase, suggesting a

rapid development of force early in the movement is desired

Table 2 13 Peak joint moments during concentric phase of CMJStudy Number of

subjectsNm NM/kg

Hip 295 5 40Aragon-Vargas & Gross (1997) 52 Knee 220 8 3 0

Ankle 244 8 33Hip 403 0 48

Bobbert et al (1987a) 10 Knee 3140 37Ankle 263 0 3 1Hip 3130 4 2

Fukashiro & Komi (1987) 1 Knee 153 0 2 1Ankle 125 0 1 7Hip 227 0 30

Ravn et al (1999) 6 Knee 438 9 5 8Ankle 98 4 1 3Hip 152 8 22

Rodano & Roberto (2002) 9 Knee 138 8 2 0Ankle 113 0 1 6

An additional joint kinetic parameter that has been examined in biomechanical studies

of vertical jumping is peak joint moment, which provides a dynamic measure of the

functional strength available to an individual during jumping The magnitude of peak

joint moment is approximately balanced between joints in the study by Aragon-

Vargas and Gross (1997a) (table 2 12) However, the single subject in Fukashiro and

Komi (1987) had a peak hip moment nearly 2 5 times that of the ankle, while Ravn et

al (1999) observed an average peak knee moment nearly 4 5 times that of the ankle

joint In light of the inter-subject variability observed in other studies (Aragon-

Vargas and Gross, 1997a, Rodano and Roberto, 2002), the magnitudes observed by

Fukashiro and Komi (1987) may be particular to that individual Three of the six

29

subjects in the study by Ravn et al (1999) were professional ballet dancers who

performed numerous jumps daily with the trunk held vertical for aesthetic reasons,

thus increasing the required contribution of knee extensors within these jumps This

may have provided a training effect resulting in the ability to achieve a greater knee

joint moment

Aragon-Vargas and Gross (1997a) found that peak hip joint moment was the best

joint moment predictor of jump height (r = 0 524) and they also included many

multiple regression predictor models No knee or ankle moment parameters were

evident in any of the regression models reported However, there was an abundance

of knee power and isometric knee joint strength parameters within the models In

light of the significant correlation that was observed between isometric knee strength

and dynamic knee moments during jumping (Aragon-Vargas and Gross, 1997a, Jaric

et al, 1989), it is possible that knee moment parameters may have been obscured for

statistical reasons However, at an individual level, where strength parameters were

not included, peak knee joint moment was significantly correlated with jump height

for one of the representative subjects (subject W r = 0 35, p < 0 015) (Aragon-Vargas

and Gross, 1997b) Peak joint moment in vertical jumping needs further examination

without the interaction of other variables, to determine whether a relationship with

jump height exists

The joint moment when angular motion of the joint reverses direction, termed joint

reversal (JR) (Aragon-Vargas and Gross, 1997a) was proposed as important in the

utilisation of the SSC in vertical jumping (Bosco and Komi, 1979) and influences the

total positive impulse during the concentric phase (Bobbert et al, 1996) Aragon-

Vargas and Gross (1997a) found hip moment at JR to be significantly correlated with

jump height (r = 0 48, p < 0 001) and was evident in several of the best predictor of

jump height at a group level Hip moment at JR was also evident in one of the three

best regression models for two of the three individuals (Subject A and Subject W)

(Aragon-Vargas and Gross, 1997b) However, due to the statistical methodology

employed in both studies, it is unknown if a relationship with any other joint moment

at JR was present As is evident from the studies outlined in table 2 14, joint

moments at joint reversal are similar in magnitude to peak joint moments (table 2 13)

If a correlation between joint moment at JR and peak joint moments exists, the

30

inclusion of a peak joint moment within a model including joint moment at JR may

not occur

Table 2 14 Joint moments at time of joint reversal in the CMJStudy Number of

subjectsNm Nm/kg

Hip 280 3 3 77Aragon-Vargas & Gross (1997) 52 Knee 206 1 2 77

Ankle 215 3 2 90Hip 403 0 4 75

Bobbert et al (1987a) 10 Knee 3140 3 70Ankle 263 0 3 10Hip 330 0 4 15

Bobbert et al (1996) 6 Knee 289 0 3 63Ankle 220 0 2 76

Table 2 14 outlines four studies that have monitored peak joint power In all the

studies reviewed, peak power of the hip joint is lower than that of the knee and ankle

In contrast, Gregoire et al (1984) found the power in the knee joint to be less than that

of the hip and the ankle, but the magnitude of the differences was not provided

Table 2 15 Peak joint power during concentric phase of the CMJStudy Number of

subjectsW W/kg W/BW

Aragon-Vargas & Gross (1997) Hip 1204 16 2 1 6552 Knee 1487 20 0 2 04

Ankle 1916 25 8 2 63Bobbert et al (1987a) Hip 1524 180 1 83

10 Knee 2549 30 1 3 06Ankle 2449 28 9 2 94

Rodacki et al (2001) Hip 1 2820 Knee 1 70

Ankle 1 87Rodano & Roberto (2002) Hip 513 73 0 74

9 Knee 982 13 9 1 41Ankle 834 11 8 1 20

As peak whole body power was found to be better correlated with jump height than

peak vGRF (Dowling and Vamos, 1993, Harman, 1990), the same may hold true at

the segmental level, however, segmental peak power may not be as strongly related to

jump height due to ineffective energy transfer between segments (Dowling and

Vamos, 1993) Aragon-Vargas and Gross (1997a) found peak hip power to be the

best single segmental predictor of jump height (r = 0 67) at a group level and in two

31

of the three individuals examined (subject B r = 0 6, subject W r =0 44) (Aragon-

Vargas and Gross, 1997b) The group model was not representative for all

individuals Peak hip power was only reported to be a significant predictor for only

five of the eight individuals examined (Aragon-Vargas and Gross, 1997b) Peak knee

power was also evident in prediction models at a group level, while ankle power was

not as relevant (Aragon-Vargas and Gross, 1997a) In contrast, at an individual

subject level, ankle power was included regression models for two of the three

individuals (subject A and subject B) and was the best single predictor for vertical

velocity at take-off for the other individual (subject W) (Aragon-Vargas and Gross,

1997b) However, while the prediction model for the subject B suggested a positive

relationship between peak ankle power and jump height, a negative relationship was

presented for subject A In light of the problems associated with multiple regression

(Section 2 1 4), the relationship between individual joint powers and jump height

from these models is unclear Peak hip power and peak hip moment were found to be

the best segmental predictors of jump height at both a group and an individual level

(Aragon-Vargas and Gross, 1997a, b) Due to the correlation observed between joint

isometric kinetics (Jane et al, 1989) and the effect of inter-joint forces and power flow

(Zajac, 1993), possible interaction between joint kinetic parameters may exist This

interaction between variables may introduce multicollmearity and would potentially

impede the entry of significant parameters into the regression models in the studies by

Aragon-Vargas and Gross (1997a, b) For this reason the effect of changes in joint

kinetics with respect to jump height needs to be examined in isolation for each

variable

Since the sum of work done by all the lower extremities approximates total work

done, it would be of interest to know how much work is done at individual joints

Table 2 15 outlines three studies detailing the amount of work done at each joint The

data provided by Bobbert et al (1986a) for the CMJ was dividend into two groups

based on subsequent performance of a DJ, both groups performed the same skill in the

CMJ The greatest amount of work done appears to be done at the hip joint This is

not surprising given that the greatest muscle mass crosses hip joint In addition to

knowledge of the magnitude of work done at each joint, the relative contribution of

each joint to total work done may provide additional insight into the movement

32

Table 2 16 Absolute amount of work performed by the joints during the concentric phase in the CMJ____________________________________________Study Number of

subjectsJ J/kg

6 Hip 234 3 1counter Knee 193 26group Ankle 171 23

Bobbert et al (1985a) 7 Hip 189 25bounce Knee 163 2 1group Ankle 158 2 1

Hip 340 46Fukashiro & Komi (1987) 1 Knee 116 1 6

Ankle 102 1 4Hip 188 24

Hubley and Wells (1983) 6 Knee 330 4 1Ankle 161 20

Note Counter group utilised amplitude of movement of the BCOM in DJ comparable to the CMJ while a reduced amplitude with a shorter concentric phase was used in the Bounce group

(2 2 5 Relative segmental contribution

Knowledge of the relative contribution of a muscle group to the total force or work

done is necessary to objectively define which muscle group is dominant at both a

group level and for a given individual for a task (Hubley and Wells, 1983) Several

techniques have been used to establish the relative contribution of individual joints in

vertical jumping Segmental techniques (Luhtanen and Komi, 1979, Miller and East,

1976) are influenced by the mass of the segment, therefore the importance of the

trunk may be over estimated Luhtanen and Komi (1978) alternatively examined the

contribution of individual joints to total impulse by examining the impulse developed

in jumps involving each joint moving in isolation and concluded knee extension

contributed 56% Under these highly constrained movements this result is hardly

surprising, since of all the conditions, knee extension moved the BCOM through the

greatest distance

An alternative approach to examining the contribution of each joint to vertical

jumping was employed by Bangerter (1968) This involved altering the strength

levels of the extensor muscles about each jomt Subjects undertook an eight-week

training program focusing on one of the extensor muscle groups, included in the

33

experiment was a control group and one group exercising all leg extensors Of the

single muscle exercise groups Bangerter (1968) found that increases in strength of the

hip and knee extensors resulted in a greater increase in height jumped, concluding that

knee and hip extensors contribute most to vertical jump achievement However, no

direct measurement of the mechanism of the enhancement was made

The amount of mechanical work performed at each joint has commonly been used to

determine the relative contribution of individual joints (Bobbert et al, 1986a,

Fukashiro and Komi, 1987, Hubley and Wells, 1983) (table 2 17)

Table 2 17 Relative contribution of each joint to total work during concentric phase of the CMJ

Study Number of Joint Percentagesubjects contribution

6 Hip 39counter Knee 32group Ankle 29

Bobbert et al (1986a) 7 Hip 37bounce Knee 32group Ankle 31

Fukashiro & Komi Hip 51(1987) 1 Knee 33

Ankle 16Hubley and Wells Hip 27(1983) 6 Knee 49

Ankle 23Nagano et al (1998) Hip 41

6 Knee 12Ankle 47

Robertson & Fleming 6 Hip 40(1987) (4 male, Knee 24

2 female) Ankle 36

Hubley and Wells (1983) showed the relative contribution to work done by each joint

during the concentric phase of the CMJ to be approximately 28%, 49% and 23% for

the hip, knee and ankle respectively While the knee was the main contributor, the

combination of the other two joints cannot be discounted as they made up

approximately 51% of total work done However, this pattern did not hold true for

every subject, with relative contribution for the knee ranging from 69% to 28% The

decrease in the relative contribution of the knee was normally accommodated by an

increase at the hip, with the ankle showing least change In contrast, Robertson and

34

Fleming (1987) found the knee extensors to contribute least toward work done, 24%

compared to 40% and 36% for hip and ankle, respectively Given the inter-subject

variability in the pattern observed by Hubley and Wells (1983) and the fact Robertson

and Fleming only examined 3 subjects (two female, one male), it is possible these

subjects were uncharacteristic of the general population In addition, it should be

noted that an increase in work done does not necessarily equate with an increase in

jump height If a greater ROM is employed, greater work must be done to jump the

same height

2 2 6 Rate of force development (RFD)

Not only is the magnitude of force development important in maximising vertical

jumping height, the ability to generate force rapidly is purportedly a major component

(Kraemer and Newton, 1994) Siff and Verkhoshansky (1998) suggest that for

ballistic movements peak force needs to be as high as possible and achieved as

quickly as possible Additionally, they contend that in exercises such as jumping,

which involve a combination of both eccentric and concentric muscular work, the

ability to generate high forces in the transition from eccentric to concentric work is

also important To examine the rate of force development (RFD) the slope between

two predetermined points of the force-time curve (Dowling and Vamos, 1993,

Häkkinen et al, 1991) or the time to reach a certain force has been used (Matavulj et

al, 2001, Ugarkovic et al, 2002) Maximal RFD has been examined through analysis

of the steepest slope of the force-time curve (Dnss et al, 1998, Paasuke et al, 2001,

Wilson et al, 1995) Jane et al (1989) used the exponential coefficient of the force

curve While vertical jumping is a dynamic movement, the RFD has typically been

quantified by means of isometric strength testing of isolated joints (Jane et al, 1989,

Paasuke et al, 2001, Tomioka et al, 2001) Contrasting findings have been observed

for the relationship between the RFD and jump height Jaric et al (1989) found

significant correlations between RFD at all three lower extremity joints and jump

height (hip r = 0 54, knee r = 0 46, ankle r = 0 38, all p< 0 05) Paasuke et al (2001)

found the peak RFD of the knee joint to be significantly correlated with CMJ height

(trained r = 0 83, untrained r = 0 79, both p <0 05) Marcora and Miller (2000)

found the isometric RFD of the knee joint was correlated with CMJ height when a

35

knee angle of 120° was tested (r = 0 69, p <0 05) but not for a knee angle of 90° (r =

0 37, p >0 05) Driss et al (1998) found the time interval from 25% peak force to 50%

peak force was correlated with jump height for the left leg (r=-0 63, p <0 01) but was

not for the right leg (r=0 15, p>0 05) In contrast, Driss et al (1998) found no

relationship between isometric knee extension maximum RFD (steepest slope over

20ms) and jump height (0 20 < r < 0 30, p >0 05) Similarly, Izquierdo et al (1999)

found no correlation between maximum RFD and CMJ height for young or middle

aged men (0 07 < r < 0 29) The RFD, measured as the time interval between 10%

and 90% peak force was not found to be correlated with jump height (Matavulj et al,

2001, Ugarkovic et al, 2002)

However, even if isometric RFD does correlate with jump height, the use of isometric

strength testing to determine the RFD of muscle groups to predict performance of a

dynamic movement, such as vertical jumping, is problematic Firstly, the question

arises over which joint angle should be used to predict performance of a dynamic

movement which utilises a relatively large range of joint motion (Kraemer and

Newton, 1994) Secondly, power flows between joints in dynamic movements and

the efficacy of this power flow has been proposed to be important for success in

vertical jumping (Gregoire et al, 1984) Isometric strength testing is a uniarticular

action where power flow is negligible Thirdly, jumping is a multiarticular movement

which involves leg extensors contracting in a coordinated fashion and requires

stabilising action of the trunk and pelvis (Young, 1995) In contrast, with isometric

testing other joints are maintained stable throughout testing procedures Finally, the

CMJ involves both eccentric and concentric contractions, which differs from the

muscular contraction employed in isometric tests, where some authors found

correlations with jump height

The importance of RFD in the CMJ itself needs to be examined, only one study

appears to have done this Dowling and Vamos (1993) examined the average slope of

the force-time curve from the minimum value to peak value but found no significant

correlation with jump height (r = 0 027, p > 0 01) However, only onejump was

undertaken for each subject, Rodano and Roberto (2002) found that at least twelve

samples were needed to find a representative value of jump kinetics Additionally,

36

Dowling and Vamos (1993) only examined whole body RFD, the RFD at an

individual joint may still be important and needs to be examined

Wilson et al (1995) used a modified smith machine positioned over a force platform

to measure whole body dynamic RFD during a CMJ They defined RFD as the force

developed over 30ms, the impulse over 100ms and the steepest gradient of the force

time curve over 5ms The maximum RFD in the CMJ was not found to be correlated

with the RFD in an isometric squat test (0 33 < r < 0 36, p >0 05) However, the

authors did not examine whether either the dynamic RFD or the isometric RFD

correlated with CMJ jump height

A number of other measures of the RFD have been put forward explosive strength,

reactive strength and reactive coefficient Siff and Verkhoshansky (1998) defined

‘explosive strength’ as the ability to produce maximal force in a minimal time and is

measured as peak force divided by the time taken to reach it The ability to use the

SSC effectively has been termed ‘reactive strength’ (Young, 1995) or ‘reactive

ability’ (Siff and Verkhoshansky, 1998) The RFD with respect to body weight was

termed ‘Reactivity Coefficient’ (Siff and Verkhoshansky, 1998) The slope of the

force up to half the maximum force and the slope from half to peak force was also put

forward as a measure of RFD (Siff and Verkhoshansky, 1998) However, no studies

appear to have directly investigated the importance of these measures to jump height

37

2 2 7 Enhancement of jump height due to countermovement

The squat jump is seen as a purely concentric action, however, exercises seldom

involve isometric, concentric or eccentric contractions in isolation (Komi, 2000) In

many movements body segments are subject to external forces such as gravity acting

on the muscles as they lengthen This lengthening phase, where the muscles are

acting eccentrically, is often followed by a concentric action of the muscle This

forms a natural type of muscle function called the stretch-shortening cycle (SSC)

(Komi, 2000, Bosco et al, 1981) The SSC has been shown to enhance performance

compared to the concentric contraction alone (Bosco and Komi, 1979, Bosco et al,

1981, Bosco et al, 1982, Cavagna, 1977) In the CMJ the extensor muscles of the

lower extremities act eccentrically to actively resist the downward movement during

the countermovement

There is ample evidence of jump performance being improved by the use of a

countermovement (Asmussen and Bonde-Petersen, 1974, Bobbert et al, 1996, Bosco

and Komi, 1979, Bosco et al, 1982b, Fukashiro and Komi, 1987, Harman et al, 1990)

Reported increases in jump height achieved in the CMJ over that of the SJ have

ranged from 1 7cm (Harman et al, 1990) to 14cm (Fukashiro & Komi, 1987)

Comparison between the SJ and the CMJ provides insight into the mechanisms of

enhancement due to the countermovement in the CMJ There have been a number of

explanations put forward for this enhancement

The freely chosen starting position of the BCOM during SJ is higher than the

minimum height of the BCOM attained during the push-off in the CMJ (Bobbert et al,

1996, Harman et al, 1990), reducing the distance over which force can be produced,

therefore reducing the distance over which the BCOM can accelerate However,

Bobbert et al (1996) found that when a comparable starting position to that of the

CMJ was utilised in the SJ the height achieved was still less that of the CMJ

Moreover, when a lower position of the BCOM than that of the CMJ was utilised

prior to the concentric phase in a SJ, Bobbert et al (1996) found that the jump height

was still on average 3 2 cm less than the CMJ

38

2 2 7 1 Enhancement of mechanical variables

Given that the CMJ will result m greater jump height than the SJ, it follows that a

more effective use of the countermovement may result in a greater jump height in the

CMJ Many mechanical factors have been shown to be greater in the CMJ than the SJ

including peak ground reaction force (Fukashiro and Komi, 1987), force at the start

of the concentric phase (Bobbert et al, 1996), average force during the concentric

phase (Bosco et al, 1981) and mechanical work done (Asmussen and Bonde-Petersen,

1974, Fukashiro and Komi, 1987, Hubley and Wells, 1983) However, the

relationship between varying use of the countermovement and jump height

achievement has not been fully examined

The average positive force difference between the CMJ and the SJ has been used as a

reflection of the mechanical enhancement due to pre-stretching of the muscles (Bosco

et al, 1981, Bosco et al, 1982a) Bosco et al (1981) found that for jumps of similar

knee amplitude (mean 71°), the average positive force was 66% greater in the CMJ

compared to the SJ Bosco and Komi (1979) found a 40% greater average force with

a larger sample (34 PE students) Possible reasons for the lower differences observed

by Bosco and Komi (1979) were i ) the knee amplitude was not controlled between

the SJ and the CMJ, and 1 1) with the use of power athletes in the study by Bosco et al

(1981) in comparison to merely physical education students by Bosco and Komi

(1979), the power athletes may have been able to utilise the countermovement more

effectively When examining the effect of knee amplitude on enhancement, Bosco et

al (1982a) found the average force enhancement associated with the CMJ over the SJ

was 49% and 75% for large (SJ 87 3°, CMJ 89 2°) and small knee (SJ 55 3°, CMJ

51 3°) amplitudes, respectively

There is a greater enhancement of average concentric force in the CMJ over the SJ

when a larger force is developed at the end of the eccentric phase (Bosco et al, 1981,

Bosco et al, 1982) The enhancement of average force has been found to be greater

the larger the instantaneous force at the end of the stretch (r = 0 5 1 , p < 0 001) and the

faster the pre-stretch of the muscle (r=0 53, P<0 001) (Bosco et al, 1981)

39

Average power has also been found to be higher during the CMJ in comparison to the

SJ (Bosco et al, 1981, Bosco and Komi, 1979, Harman et al, 1990) Enhancements

of between 81% (Bosco et al, 1981) and 15% (Harman et al, 1990) have been

observed in the CMJ over that of the SJ However, as knee angle was not controlled

between the SJ and the CMJ these enhancement values may be misleading Harman

et al (1990) however, did not find any significant difference in peak force or peak

power between the CMJ and the SJ

Since the vGRF is a function of individual joint forces, greater insight may be gained

from examination of joint kinetics Two studies compared the joint kinetics of the

CMJ and SJ (Hubley and Wells, 1983, Fukashiro and Komi, 1987) Fukashiro and

Komi (1987), when testing a single individual subject, found total mechanical work

done by the subject during concentric phase of the CMJ was 25% more than the work

done during the SJ The amount of work done at the knee and ankle joints was similar

between the CMJ and the SJ, and the increase in work was brought about by extra

work done at the hip The amount of extra work done at the hip was 116J of the 132J

of total extra work done, corresponding to 88% of the total extra work done in the

CMJ In contrast, Hubley and Wells (1993) found no significant difference at a group

level between the total amount of work done during the concentric phase of the CMJ

to that of the SJ, and at the segmental level no clear enhancement pattern was

observed when knee flexion amplitude was controlled At an individual level, for one

subject the enhancement ratio for the hip and knee joints were 1 23 and 0 79,

respectively, while for another subject the opposite pattern was observed with ratios

of 0 76 and 1 96 for the hip and knee joints respectively The rank order of magnitude

of work done by the joints (hip-knee-ankle) was maintained for the single subject in

the study by Fukashiro and Komi (1987) for both the SJ and the CMJ but the pattern

was only maintained for 3 of the 6 subjects in the study by Hubley and Wells (1983)

2 2 7 2 Possible mechanisms for enhancement

Enhancement in the performance outcome, and the average concentric force and work

done that produces it has been attributed to a number of factors greater force at the

start of the concentric phase (Bobbert et al, 1996), storage of elastic energy (Bosco

and Komi, 1979, Bosco et al, 1981), contractile component “potentiation” (Cavagna,

40

1977), spinal reflex of the muscles (Bobbert et al, 1996) and better control of

movement (Bobbert et al, 1996) Each of these factors is briefly outlined below

Force at the start of the concentric phase

In general, during maximum muscle contractions it takes time before peak force can

be reached This is due to the finite rate of muscle stimulation by the central nervous

system, the time constants of the stimulation-active state coupling and the interaction

between the contractile elements and series elastic elements (Bobbert et al, 1996) If

the active state of the muscle only begins to rise at the start of the concentric

contraction, part of the shortening distance is travelled at a sub maximum level,

resulting in less work done The muscle may build up a maximum active state by

isometric contraction or as a result of an eccentric contraction via a countermovement

Therefore, a higher level of force can be achieved in the muscles at the start of the

concentric phase in the CMJ in comparison to the SJ (Bobbert et al, 1996) In

consequence this facilitates greater work done during the CMJ than the SJ Bobbert et

al (1996) found greater moments at the hip, knee and ankle at the start of the

concentric phase in jumps involving a countermovement phase in comparison to a SJ,

even when the body position at the start of the concentric was the same They

concluded the increase in force at the start of the concentric phase provided the

majority of the enhancement

However, attributing the enhancement in the total amount of work done in the

concentric phase to a greater amount of force at the start of the concentric phase may

be misleading Walshe et al (1998), with the use of an isokinetic squatting machine,

compared the work output of an isokinetic contraction preceded by three differing

forms of muscular contraction, isometric, SSC and rest The SSC condition involved

the subject making downward movement similar to that of the CMJ prior to the

isokinetic contraction In the isometric condition the force and knee angle was

matched to those experienced at the start of the concentric phase in the SSC condition

(mean force at start of concentric phase isometric 1169N, SSC 1193N, not

significantly different) More work was done in the first 300ms following the pre­

stretch in the SSC condition compared to the isometric condition Additionally, a

greater amount of power was developed earlier in the movement They concluded

that not only the amount of force developed at the start of the concentric phase was

41

important but also the manner in which it was developed Enhancement factors

relating to the active pre-stretch of the muscle prior to the concentric phase are

outlined below

Storage of elastic energy

The enhancement in jump performance has also been attributed to the release of

elastic energy stored in the muscle during the eccentric phase, which is reutilised

during the concentric phase (Bosco et al, 1981, 1982, Cavagna et al, 1965, 1968)

The eccentric contraction of the muscle causes storage of elastic energy in the series

elastic component, mainly the protein titin, the tendons and the cross-bridges (Bosco

& Komi, 1979) The myosin filaments are rotated backwards against their natural

tendency during the stretch to a position of higher potential energy This in essence

causes mechanical work to be stored in the sarcomere cross-bridges that can be reused

during the concentric phase, provided the muscles are allowed to shorten immediately

after the stretch (Bosco et al, 1982a)

Potentiation

Improvement in performance may also be due to the stretching of active muscle

during the eccentric phase, which alters the contractile machinery of the muscle

(Bobbert et al, 1996), referred to as “Potentiation” or the “Cavagna effect “ (Cavagna,

1977) The exact means by which the contractile machinery is altered does not appear

to have been fully explained

Spinal reflex

Active stretching of the muscles during the eccentric phase may trigger spinal

reflexes, as well as longer-latency responses, which increase muscle stimulation

during the concentric phase (Bobbert et al, 1996) With the increased stimulation the

muscles can produce higher forces and thus greater work can be done during the

concentric phase

These enhancements are possible provided the muscles are allowed to shorten

immediately after the stretch (Bosco et al, 1982a) The lengthened cross-bridges can

become detached if the stretch is maintained for too long, or may cause sarcomere

“slipping” if the range of stretch is too great (Bosco et al, 1981) Therefore the

42

transition period between the eccentric and concentric phase, called “coupling time”

(Bosco et al, 1981) must be kept short A negative correlation (r =-0 35, p < 0 01) has

been found between the enhancement in average force in the CMJ over that of the SJ

(Bosco et al,1981)

Bosco et al (1981) found coupling time to last on average 23 0±14 7ms in the CMJ

and increased with greater the movement amplitudes (r = 0 46, P<0 001) Bosco et al

(1982a) found coupling times of 18 9ms and 44ms corresponding to knee angular

displacements of 55 3° and 87 3 0 respectively Coupling time was reduced with

greater force in the eccentric phase (r = -0 47, P<0 001), as the increases in stiffness

made the transition from the eccentric to the concentric phase take place faster (Bosco

et al, 1981)

Variations in the relative amount of muscle fibre type between individuals have been

proposed as a possible reason of differences in response to effective utilisation of the

SSC between individuals (Bosco et al, 1982a) Fast twitch (FT) and slow twitch (ST)

muscle fibers are characterized by different visco-elastic properties resulting in

different response to the SSC, depending on the speed of movement (Bosco et al,

1982a) Bosco et al (1982a) found significantly greater force at the start of concentric

phase for subjects with more fast twitch fibers in jumps of small amplitude (FT =

30 2±4 8 N kg 1 and ST 25 9±4 8 N kg \ p<0 05) but no difference was found for

jumps of large amplitude A positive correlation between the %FT and the force at

the start of concentric phase for small amplitude jumps was evident (r = 0 57,

p<0 05), but no relationship was present for large amplitudes Despite the difference

in the force at the start of the concentric phase, the relative (percentage) enhancement

of force between CMJ and SJ did not differ with fiber type in small amplitude jumps

However, there was a greater relative enhancement in jump height with large

amplitudes for individuals with a predominance of slow twitch fibres Bosco et al

(1982) suggested that since the eccentric phase of small amplitude jumps is short, the

greater force at the start of the concentric phase in the FT group is due to faster

recruitment of motor units The duration of the eccentric phase, which was relatively

long (mean 147ms) was not a limiting factor in jumps of large amplitude, allowing ST

fibres enough time to be stimulated The reason for differences in relative

enhancement of force between groups was attributed to the attachment-detachment

43

cycle of the sarcomere cross-bridges For small amplitude jumps the coupling time

was small (18 9±10 7ms) and was unlikely to be a limiting factor for either fiber

types Jumps of larger amplitude are characterized by longer coupling times

(44 0±16 8ms) which favours ST fibres as they retain their cross-bridge attachment

longer However, a greater number of fibres detach in the FT fibre group, resulting in

greater relative utilization of store energy in the ST group

Control of movement

One additional explanation for greater height achieved in the CMJ than the SJ is that

the squat jump is a less practiced movement (Bobbert et al, 1996) If a non-optimal

control is selected it may affect the movement pattern, resulting in the amount of

work done by the muscles being transformed to effective energy being submaximal

(Bobbert et al, 1996)

2 3 Coordination

The human movement system is made up of many subsystems including the neural,

perceptual and muscular-skeletal systems A motor task is the result of the central

nervous system sending impulse volleys to the muscles in light of the expected and

actual mechanical demands of the task (Bobbert & van Ingen Schenau, 1988)

Coordination has been the focus of both biomechanical and motor control

neuroscience studies Biomechanical studies have centred on examining how body

segments and muscles interact to perform motor tasks (Hudson, 1986) in order to

explain how performance is enhanced or injuries occur (Hamill et al, 1999, Schache et

al, 1999)

The previous section (2 2) reviewed studies, which investigated the magnitude of the

mechanical output of the lower extremities in vertical jump performance However,

mechanical output in maximum effort multi-joint movements is not simply a

reflection of the mechanical capacity of the neuromuscular system’s ability to produce

force but also dependent upon the coordination pattern employed to effectively utilise

the work capacity of the muscles (Tomioka et al, 2001, Walshe et al, 1998)

Coordination is the process where the multiple and different component parts of a

44

system are brought into proper alignment in temporal space and time (Turvey, 1990)

and refers to the timing and sequence of segmental movements Therefore it is

necessary to examine both the muscle mechanical output and the coordination pattern

employed to gam a comprehensive insight in to the factors effecting jump

performance

The importance of both coordination and mechanical capacity in vertical jumping has

been highlighted m three separate studies, which used forward dynamic control

models of vertical jumping Bobbert and Van Soest (1994) increased peak isometric

force in all lower extremity muscles resulting in an increase in jump height, but only

when the pattern of muscle activation was re-optimised When the muscle activation

pattern from the original neuromuscular capacity was used, the jumping movement

was disrupted, resulting in a lower jump height than that with the original

neuromuscular capacity Nagano and Gerritsen (2001) altered peak isometric muscle

force, peak muscle shortening velocity and the number of motor units recruited, and

re-optimised the muscle activation pattern with each alteration The optimal timing

pattern of muscle activation changed with each alteration of the neuromuscular

parameters The change was greatest with alterations of peak isometric muscle force

and not so evident for shortening velocity When the optimal muscle activation

pattern from the original model was applied to the model with altered strength,

enhancement of jump height was only 14 15cm, compared to 16 62cm when re­

optimisation had occurred Finally, Pandy et al (1990) showed with the use of an

optimal control model that when the activation of the vasti (knee extensor) was

delayed by 10%, vertical jump height was significantly reduced The trunk rotated

past the vertical and the angular velocity of the thigh was reduced, resulting m the

joints not being fully extended at take-off In light of the results of these three studies

it is possible that in addition to examination of mechanical output variables, the

variation in the patterns of coordination may also reveal and explain differences in

jump performance

2 3 1 Constraints influencing movement pattern

For a given movement task many constraints are imposed on the system Under the

dynamics systems framework functional patterns of coordination emerge under task,

45

information and environmental constraints of the neuro-musculoskeletal system that

places a requirement on the system to change it’s organizational state (Davids et al,

2000) Constraints are defined as specific requirements of an anatomical, neuronal or

biomechanical origin, which impose restrictions on the possible muscle actions of the

movement system (Jacobs and van Ingen Schenau, 1992) These constraints provide

the limits or conditions for the self-organising processes, reducing the possible

movement combinations (Clark et al, 1989) Dealing with these constraints is an

important goal in the organisation of muscle actions (Bobbert and van Ingen Schenau,

1988) and should be considered when examining vertical jumping performance

Some mechanical constraints that influence the coordination pattern in vertical

jumping are outlined below

Intersegmental dynamics

A force generated by a muscle will not only cause acceleration at the joint it spans but

also other joints due to the dynamic coupling arising from the multi-articular nature of

the body (Zajac et al, 2002) An example of this is in flat foot standing near vertical

posture, the soleus can act to accelerate the knee into flexion by accelerating the thigh

and shank into extension even though it only spans the ankle This is achieved due to

inertia forces being transmitted from one segment to another via joint reaction forces

(Zajac, 1993)

Task constraint

During the flight phase, neglecting energy losses due to air resistance, the effective

energy of the BCOM remain constant The effective energy refers to the sum of

kinetic energy and potential energy (Bobbert and van Ingen Schenau, 1988) The aim

of the jump is to maximise the effective energy at take-off, the kinetic energy depends

on vertical velocity of the BCOM at take-off, while potential energy is dependent on

height of the BCOM above the ground at take-off (Bobbert and van Soest, 2001) The

aim is to maximise effective energy as a whole and not one element at the expense of

the other

The vertical velocity of the BCOM is most strongly affected by the vertical velocity

of the centre of mass (COM) of the upper body, as the upper body has the greatest

relative mass During the first part of the jump the increase in vertical velocity of the

46

COM of the upper body is mainly due to the vertical velocity difference between the

upper body COM and the hip joints The difference reaches a peak at about 190ms

before toe-off, with relatively constant angular velocity thereafter (Bobbert and van

Ingen Schenau, 1988) At this point the hip joint has moved through 20°, which is

only part of the shortening range and work capacity of the hip joint If extension of

the lower legs was not possible the effective energy of the BCOM would plateau and

take-off would occur soon after However, extension of the lower legs is possible and

it is at this point that the knee joint begins to extend Extension of the knee joint

increases the vertical velocity difference between the hip and the ankle, which

exceeds the decline in the velocity difference between the upper body’s COM and the

hip joints, thus enabling the vertical velocity of the upper body’s COM to increase

However, in spite of increasing angular velocity of the knee joint, the velocity

difference between the upper body’s COM and the ankle joint peaks at 60ms before

take-off At this instant the knee angle is only approximately at 125° on average, far

from maximum extension and only part of the knee’s work capacity is used Again

the effective energy would plateau if no plantar flexion were possible However,

plantar flexion is possible and increases the vertical velocity difference between the

ankle and the metatarsal heads, again this exceeds the decrease in vertical velocity

difference between the upper body’s COM and the ankles, allowing the vertical

velocity of the upper body’s COM to continue to increase At about 30ms before

take-off the vertical velocity difference between the ankle and the metatarsal head

reaches a peak (Bobbert and van Ingen Schenau, 1988) It is flexion of the toes that

stops ground contact from being lost prematurely but at this stage the magnitude of

the vGRF is below body weight so decrease in the vertical velocity is inevitable It is

suggested that in order to maximise performance the vertical velocity difference

between ends of each segment should peak in a proximal-to-distal sequence (Hudson,

1986) In this way it is hypothesised that uniarticular hip extensors, knee extensors

and plantar flexors shorten over their full range and release as much energy as

possible to contribute to the body’s effective energy at take-off (Bobbert and van

Ingen Schenau, 1988)

Anatomical constraint

To prevent injury associated with hyperextension of the joints, the joint’s angular

velocity has to decelerate to zero at full extension This has been described as an

47

‘anatomical constraint’ (Van Ingen Schenau et al, 1987) If uniarticular muscles were

only available to decelerate the segments, continued contraction of the extensor

muscles towards full extension of the joint would not only be wasteful, but would also

be dangerous, as structures that traverse the joint would run the risk of damage

(Bobbert and van Ingen Schenau, 1988) Additionally, power would be lost to heat

due to excessive eccentric contraction of the flexor muscles (van lngen Schenau et al,

1987) Biarticular muscles play an important role in not only decelerating a joint, but

also transferring energy to a more distal joint to aid in joint extension For example,

the biarticular gastrocnemius muscle plays an important role toward the end of the

propulsion phase by decelerating knee extension and increasing plantar flexor

moments (van Ingen Schenau, 1987)

Geometrical constraint

The aim of the concentric phase is to attain the maximum vertical velocity of the

BCOM at take-off The only way to generate linear velocity is to give the segments

an angular velocity (Bobbert and van Soest, 2001) The amount the rotation of a

segment contributes to the position of the BCOM is dependant on geometric factors

Figure 2 3 shows a segment with proximal end p , distal end of and length /

The vertical difference between p and d is given by

(yp-yd) = / s i n #

where / is the distance between p and d, while 0 is the angle the segment’s

longitudinal axis makes with the horizontal The vertical velocity difference between

p and d is given by

(y P - V d ) = I COSO)

where to is the angular velocity of the segment and v is linear velocity

Figure 2 3 Geometrical configurations of typical segment

48

When 0 is 90°, the vertical difference between p and d is I (since sm 0 = 1) and the

velocity difference is zero no matter how high the angular velocity is (since cos © =

0) As a result the vertical velocity difference between the segment end points may

peak and decline in spite of constant or increasing angular velocity Dealing with this

phenomenon is an important goal in organising muscle actions (Bobbert and van

Ingen Schenau, 1988) In vertical jumping when the knee approaches full extension

the velocity difference between the hip and the ankle will approach zero and the

transformation of knee angular velocity to translation of the BCOM will be less

effective

Vertical jumping is initiated by the acceleration of the trunk through activation of the

gluteus maximus Due to geometrical constraints the effect of the angular velocity of

the trunk on the rise of the BCOM decreases as it approaches the vertical At this

point the angular velocity of the trunk is decelerated by activation of the rectus

femons This allows the gluteus maxims to remain active while also transporting

power to the knee via the rectus femons, thus maintaining the rise of the BCOM If

the jump were performed without plantar flexion the body would leave the ground at

the instant the vertical velocity difference between the hip and the ankle reached a

maximum (Van Ingen Schenau et al, 1987) The larger body segments would pull the

smaller segments from the ground when they reached a critical velocity with respect

to the ground (Bobbert et al, 1986a) Bobbert et al (1986b) found peak vertical

velocity difference between the BCOM and the ankle joint to occur at a mean knee

angle of 128° Van Ingen Schenau et al (1987) found the velocity difference between

the hip and the ankle to peak at a mean knee angle of 132°, and the mean knee joint

angle at the start of the push-off phase to be 82° This corresponds to only 50° of a

total possible extension range of 98° (from 82° to 180°), thus a large part of the knee

extensor’s capacity to shorten and liberate energy could not be used for external work

(Bobbert et al, 1986) Due to fast plantar flexion, the hip joint can accelerate up to

25ms before take-off (Van Ingen Schenau et al, 1987), thus enhancing jump height

Moment distribution constraint

During vertical jumping the vGRF must be directed more or less vertically through

the midline of the body through the BCOM If forces are directed elsewhere the

whole body would rotate and/or energy would be dissipated horizontally This would

49

result in a significant reduction in jump height During the countermovement the

body has a tendency to rotate forward which must be counteracted by directing the

resultant vGRF vector in front of the BCOM, while in the concentric phase the body

has a tendency to rotate backwards which must be counteracted by directing the

resultant vGRF vector behind the BCOM (Voigt et al, 1995)

2 3 2 Biarticular muscles

Uniarticular muscles will always act to rotate a joint it spans in the direction of

applied muscle moment consistent to its anatomical classification However,

biarticular muscles may also act to rotate a joint in the opposite direction than the

muscle moment due to muscle moments of other joints inducing a stronger counter

angular acceleration of the joint (Zajac et al, 2002) Muscles can redistribute

segmental energy by accelerating some segments and decelerating others such that the

energy reduction due to deceleration of one equals the energy increase of the other

(Putnam, 1991, Zajac et al, 2002) Zajac (1993) suggest that in jumping, uniarticular

extensor muscles provide most of the propulsive mechanical energy, uniarticular

flexors are virtually non-contributory and biarticular muscles fine-tune the

coordination The extent to which energy transfer occurs has been controversially

viewed

In vertical jumping energy transfer is able to occur because during plantar flexion, the

knee and hip joints have high angular velocity This results in a lower shortening

velocity for the biarticular muscles than the mono-articulator muscles This allows

the biarticular muscles to deliver more force and consequently allows power

generated by the gluteus maximus to extend the knee joint through seemingly

opposing actions of the gluteus maximus and the rectus femons (van Ingen Schenau

et al, 1985) Timely activation of the rectus femons decreases the angular

acceleration of the trunk and coupled with the onset of knee extension, transfers

power from the hip to the knee A similar mechanism allows power to be transferred

from the knee to the ankle via the gastrocnemius (van Ingen Schenau et al, 1985)

During the last 20-40ms of the propulsive phase of the jump the extensor forces of the

knee and ankle reach peak velocity and are not able to deliver notable force at such

50

velocities It is the biarticular muscles, which deliver power during this period, that

exhibit relatively slow contractile velocities due to the opposing effect on muscle

length by the motion of the joints crossed (Gregoire et al, 1984)

2 3 3 Coordination in Vertical jump

The optimum coordination of a given task falls somewhere on a continuum from

sequential to simultaneous It is proposed that a task where the object is light or

where the distal end is open employs a sequential pattern (proximal to distal)

(Hudson, 1986) A proximal-to-distal sequential pattern has been found for kicking

(Davids et al, 2000), throwing (Button et al, 2003) and the volleyball serve (Temprado

et al, 1997) When the object is heavy or the distal end is closed, such as in weight

lifting, it is proposed that the optimum pattern is more simultaneous (Hudson, 1986)

Tasks where velocity is important the pattern is expected to be more sequential

However, when large forces or accuracy is required the pattern is expected to be more

simultaneous Both patterns have been hypothesised for maximal vertical jumping

(Hudson, 1986)

From vGRF data, Bobbert and van Ingen Schenau (1988) found that the BCOM rises

linearly up to about 30ms before take-off During the first part of the push-off phase,

the rise in the BCOM is primarily due to the extension of the trunk The relative

contribution of the trunk decreases in the course of the push-off as the relative

importance of leg extension increases Extension of the legs not only contributes via

a rise in the COM of the legs but mainly due to raising the hip joints, thereby

increasing the height of the COM of the upper body (Bobbert & van Ingen Schenau,

1988)

A few studies have examined the timing and sequence of electromyographic activity

of key lower extremity muscles during vertical jump performance (Bobbert and van

Ingen Schenau, 1988, Ravn et al, 1999, van Soest et al, 1985) However, it is at the

joint kinematic and kinetic level, where the final movement pathway is observed, is

the area where the coordination pattern has been most frequently examined (Bobbert

and van Ingen Schenau, 1988, Hudson, 1986, Rodacki et al, 2001) The following

51

section outlines the subsequent coordination pattern that has been observed in the

CMJ in light of the various constraints imposed on the system

2 3 3 1 Pattern of joint extension

The initiation of joint extension, also refer to as joint reversal (JR), has been reported

to occur for the CMJ in a proximal-to-distal sequence, starting with the hips, then the

knees followed by the ankles (Gregoire et al, 1984) This pattern is in close

agreement with the findings from dynamic optimisation models (Bobbert and van

Soest, 2001) One explanation for the sequential pattern observed is that all extensor

muscles are activated simultaneously but the upper body obtains additional vertical

acceleration, which exerts a downward force on the lower limb restricting extension

or even causing additional flexion Hudson (1986) found additional flexion in the

lower limbs in 13 of the 20 subjects tested However, Bobbert and van Soest (2001)

disputed this idea suggesting if a simultaneous pattern was desired in the CMJ, surely

a muscle activation pattern to achieve it would have been learnt by now

Results of electromyographic analysis also do not support the hypothesis that extensor

muscles are activated simultaneously, rather they become maximally activated in the

sequence of hip extensors, knee extensors and plantar flexors (Bobbert and van Ingen

Schenau, 1988) Bobbert and van Ingen Schenau (1988) found that m gluteus

maximus, a hip extensor muscle, was maximally active at the start of the push-off

phase, while the knee extensor, m vastus medialis, was only 62% activated and the

plantar flexor, m soleus was only 26% activated Approximately 90ms were

observed between peak activation of these muscles (m vastus medialis was 190ms

before take-off, m soleus was 100ms before take-off)

Table 2 18 Timing of joint reversal to take-off (absolute and relative to total duration)Study number of Hip Knee Ankle

subjects (s) (s) (s)Jensen et al (1994)* 6 male abs 0 28 021 0 19

rel 0 44 0 59 0 62Rodacki et al (2001) 20 male abs 0 38 0 28 0 27

rel 0 62 0 72 0 73Rodacki et al (2002) 11 male abs 0 39 031 0 27

rel 0 59 0 66 0 71Note * = data from Jensen and Phillips (1991) study

52

A proximal-to-distal sequence of joint extension has been reported for vertical

jumping (Jensen and Phillips, 1991, Rodacki et al, 2002) Rodacki et al (2001) found

the reversal of the hip joint occurred on average 100±6ms before the knee joint, which

occurred on average 7±44ms before the ankle joint However, a proximal-to-distal

pattern was not always observed, with the ankle preceding the knee in 3 of the 12

subjects In a subsequent study, Rodacki et al (2002) found delays of 74±13ms and

45±40ms between the hip and knee, and the knee and the ankle respectively While

these intervals are longer than reported by Rodacki et al (2001), the interval between

the extension of the knee and the ankle was variable and in some cases ankle

extension preceeded that of the knee Likewise, Jensen and Phillips (1991) found a

proximal-to-distal sequence on average, but this pattern was not always present

Clarke et al (1989) reported that the hip joint reversal was always before the knee for

the 12 female volleyball players and gymnasts examined Even greater variability

was evident in a study of 52 physically active male college students by Aragon-

Vargas and Gross (1997) In 23 of the subjects a proximal-to-distal pattern was

observed, however, for 21 subjects while the hip was extended first, the ankles were

extended before the knee joints The remaining 8 subjects used another pattern

including one subject utilising a distal-to-proximal sequence

Aragon-Vargas and Gross (1997a) did not find the sequence of joint reversal to be

related to jump height achieved when differences between individuals were examined

However, when differences in repetitions of a subject’s own movement was examined

the sequence of joint reversal was found to be a significant predictor of jump height

for three of the eight individuals examined (Aragon-Vargas and Gross, 1997b),

including it being the best single segmental predictor of jump height for one

individual (subject A r = 0 65, p< 0 001) Aragon-Vargas and Gross (1997a)

measured the coordination of joint reversal from a purely qualitative perspective and

did not measure the extent to which deviations from a given pattern affected jump

performance Often when a sequence is reported the time interval between events has

been within the ±1 frame measurement error (Jensen and Phillips, 1991, Rodacki et

al, 2001) Therefore, many of the results involving close occurrences of events must

be viewed with caution

53

Hudson (1986) when examining the coordination pattern of segments, found jumps

typically to be initiated with extension of the trunk (HAT) followed by the thighs then

the shank at intervals of 44ms and 39ms, respectively The interval between segment

extensions was highly variable with a range of between 170ms and 220ms for the time

difference between the trunk and thigh, and the thigh and shank, respectively The

absolute timing between the trunk and the thigh and the thigh and shank was about

50ms The pattern was not consistent for all subjects Of the 20 subjects examined, 8

initiated thigh extension prior to the HAT, 2 initiated thigh extension prior to the

trunk, while 2 extended the shank before the thigh Bobbert and van Ingen Schenau

(1988) also examined the initiation of extension of the segments and found that at a

group level the trunk began to extend 330ms before toe-off followed by the thigh

(270ms), the shank (200ms) and the foot (150ms) The time delays between the trunk

and thigh (60ms) and between the thigh and the shank (70ms) were greater than those

reported by Hudson (1986)

2 3 3 2 Timing of peak angular velocity

Maximizing velocity of joint rotations may be important from a mechanical

perspective (Bobbert and van Ingen Schenau, 1988), likewise as with timing of joint

reversal, correct timing of peak angular velocity may be necessary Hudson (1986)

found the angular velocity of the trunk was first to peak followed by the thigh and

then the shank, at intervals of approximately 29ms and 6ms, respectively Variability

was evident at the hip, but a consist coordination pattern was observed at the knee

with a range of only 30ms between the thigh and the shank Again this sequential

pattern was not observed in all of the 20 subjects, with 11 subjects reaching peak

velocity of the thigh before the trunk and one reaching peak velocity of the shank

before the thigh Bobbert and Van Ingen Schenau (1988) found angular velocity of

the trunk to peak at 190ms on average before take-off, with the rest of the segments

peaking 30ms before take-off

54

) Table 2 19 Mean timing of peak joint velocities (absolute and relative to total d u r a t i o n ) _______ ______________________________________Study number of Hip Knee Ankle

subjects _ _ (s) (s) (s)Jensen et al (1994) 6 male abs

rel0 040 0 037 0 030

Rodacki et al (2001) 20 male abs 0 080 0 068 0 080rel 0 92 0 93 0 920

Rodacki et al (2002) 11 male abs 0 074 0 066 0 067rel 0 928 0 929 0 928

Table 2 19 shows the timing of peak angular velocity of each joint for three studies

Timing of peak joints velocities appear to occur in close proximity Jensen and

Phillips (1991) found that for 5 of the 6 subjects they tested, all joint angular

velocities peaked within 12ms of each other Clarke et al (1989) also reported the

delay in peak angular velocity between the knee and ankle was on average within the

measurement error

Since segments are different lengths, rotation of each segment will contribute

differentially to the rise in the BCOM For this reason Bobbert and Van Ingen

Schenau (1988) examined the vertical velocity difference between the proximal and

distal ends of each segment A proximal-to-distal sequence was found for the peak

vertical velocity difference between proximal and distal ends of each segment

Bobbert & Van Ingen Schenau (1988) suggested that as the purpose of segmental

rotations during the concentric phase of the jump was to increase the vertical height of

the BCOM, the vertical difference between proximal and distal ends may peak and

decline in spite of constant angular velocity of the segment due to geometric factors,

dealing with this may be an important goal in the organisation of muscle actions A

proximal-to-distal pattern was observed in the peak velocity difference, with the trunk

segment peaking at 190ms before take-off followed by the thigh, shank and foot at

intervals of 80ms, 70ms and 10ms, respectively (Bobbert and Van Ingen Schenau,

1988) Aragon-Vargas and Gross (1997) also reported a proximal-to-distal sequence

in peak vertical velocity difference between the proximal and the distal ends of a

segment in 42 of the 52 subjects examined, however, no values of delay were given

55

2 3 3 3 Timing of peak joint power

The temporal delay between peak joint power and take-off in the CMJ for three

studies are outlined in table 2 20

Table 2 20 Mean timing of peak joint power prior to take-off (absolute and relative to total duration) _______________________________________________Study number of subjects Hip

_ (s)Knee

(s)Ankle

(s)Rodacki et al (2001) 20 male abs 0 300 0 113 0 090

rei 0 700 0 890 0910Rodacki et al (2002) 11 male abs 0 204 0 116 0 070

rei 0 780 0 880 0 930Bobbert et al (1986c) 10 male abs na na 0 050Bobbert and van Ingen 10 male abs 0 170 0 600 0 050Schenau (1988)

Rodacki et al (2001, 2002) found a proximal-to-distal pattern in peak joint power in

the CMJ, with delays of approximately 100ms observed between joints Low

variability was observed at the ankle and knee suggesting a robust pattern Bobbert

and Van Ingen Schenau (1988) also found a proximal-to-distal sequence of joint

power to occur for 10 male volleyball players studied The temporal sequence in peak

joint power occur first with the hip at approximately 170ms before toe-off followed

by a delay of 110ms for the knee joint (60ms before take-off) and the ankle shortly

after at 50ms before toe-off However, the delay between the knee and the ankle was

within ±1 frame measurement error No measure of variability in timing was given,

nor was it stated if this pattern was observed in all subjects Gregoire et al (1984)

found peak power in the hips to occur before that of the ankles, however, the extent of

the delay was not stated They reported that the power of the knee joint showed a

dramatic drop in the last part of the jump, at the same instant the ankle joint peaked

56

2 3 4 Coordination as a predictor of jump height

Aragon-Vargas & Gross (1997a) found that the time difference between joint reversal

was not a significant predictor of jump height between individuals This is in contrast

to the findings of Hudson (1986) who suggested very small delays between adjacent

segments are desired, however, no correlation was give with jump performance

However, Aragon-Vargas & Gross (1997) examined only the timing between the first

and last joint reversals, while Hudson (1986) examined adjacent segments When

examining individual subjects Aragon-Vargas and Gross (1997b) did however find

the sequence of joint reversal was the best single predictor of jump height accounting

for 42% of the variation for one of the individuals and was included in a predictor

model for another individual This was purely a qualitative measure and the extent to

which the pattern varied from a proximal-to-distal sequence was not examined There

was a negative relationship between the occurrence of a proximal-to-distal sequence

and jump height, which is in disagreement with other studies where a proximal-to-

distal sequence was assumed optimal (Bobbert & van Ingen Schenau, 1988, Hudson,

1986)

Tomioka et al (2001) calculated the quadratic term of the average relative phase angle

based on the expectation that the relationship was non-linear Both the quadratic

(r=0 71, p=0 01) and linear terms (r=-0 64, p=0 03) were correlated with maximum

jump height during the concentric phase, but no relationship was found for the counter

movement phase There was no significant relationship between isokinetic knee

strength and coordination (r=0 32, p=0 31), both contributed independently to vertical

jump height This is in disagreement with finding of Bobbert and Van Soest (1994)

and Nagano and Gerritsen (2001) who with the use of dynamic optimisation models

found that that changes in strength need to be accompanied by changes in

coordination pattern to utilise the increased strength In light of the importance of

optimal coordination for a given neuromuscular capacity, the effect of changes in the

timing of key events of adjacent joints should be examined in relation to jump height

achievement

57

2 4 Training interventions to increase jump height

In vertical jumping, as in any sporting task, it is the properties of the

neuromusculoskeletal system and the control of the movement that ultimately

determine the potential performance outcome, which in the case of vertical jumping is

the height achieved (Bobbert and van Soest, 1994) Control of the movement refers to

the technique, timing and coordination of the movement (Bobbert and van Soest,

1994) and can be improved with guided repetition of the movement (Bobbert, 1990)

The properties of the neuromusculoskeletal system include anatomical characteristics

(e g mass distributions, limb length and muscle moment arms), biochemical

characteristics (e g , enzyme activities and substrate concentrations in the muscles),

physiological characteristics (e g muscle strength, muscle fibre composition)

(Bobbert and Van Soest, 1994) and neural characteristics (e g motor unit recruitment,

firing rate) Anatomical characteristics are more or less given but training may

enhance many of the biochemical, physiological and neural characteristics

Many components of the neuromuscular system have been proposed to influence

jump height achievement, both relating to the concentric phase alone and the SSC as a

single neuromuscular action The height an athlete achieves is determined primarily

by the vertical velocity of the BCOM at take-off Through the impulse-momentum

relationship, it is clear a large amount of force is required In vertical jumping the

athlete has a limited time to apply force before leaving the ground, therefore a large

amount of force must be applied as quickly as possible For this reason athletes seek

to maximise power Since power is the product of the amount of force and the

velocity of the movement, it is often reasoned that increasing the maximum amount of

force applied is all that is required of a strength training program (Plisk, 2001) There

is a clear relationship between the cross-sectional area of the muscle and the greatest

amount of force that can be produced (Fry and Newton, 2002) Once the athlete has

achieved the upper limit for specific muscle tension for a given cross-sectional area

(40-45Ncm ]) hypertrophy is required (Plisk, 2001) The most common form of

training to achieve hypertrophy is heavy resistance training involving repetition of a

load 60-80% of one repetition maximum (1RM) (Häkkinen, 2002) Wiscoff et al

(2004) found 1RM half squat to be significantly correlated with jump height (r=0 78,

p<0 02) Additionally, isometric strength has been found to be sigmfiacntly

correlated with vertical jump height (Driss et al, 1998, Eisenman, 1978, Häkkinen,

58

1991, Jane et al, 1989) in direct contrast however, a number of studies have found

no significant relationship between isometric strength and jump height (Marcora and

Millar, 2000, Paasuke et al, 2001, Young et al, 1999a), suggesting other elements of

the neuromuscular system are more important m vertical jump performance

Since the time available to apply force in vertical jumping is limited, high amounts of

force need to be applied as early in the movement as possible Therefore, training ts

often aimed at improving the RFD and to move the force-time curve up and to the left

resulting in a greater impulse during the limited duration (Plisk, 2001) In a

movement of high velocity the ability to produce force at higher velocities is

paramount Häkkinen (1991) stated that for explosive movements the principle of

specificity of training must be followed, utilising light loads which may be moved

quicker, the muscles are highly activated and contract at high velocity Both

isokinetic strength at velocities in excess of 360° s 1 (Saliba and Hrysomallis, 2001)

and RFD (Jaric et al, 1989, Marcora and Millar, 2000, Paasuke et al, 2001) have been

found to be significantly correlated with jump performance

The use of a countermovement prior to the concentric phase has been shown to

enhance vertical jump height (section 2 2 7) Pre-stretching the muscle has been

proposed to increase the amount of energy stored in the muscle (Ausmussen and

Bonde-Petersen, 1974, Bosco and Komi, 1979) and increases the neural stimulation of

the muscle via the stretch reflex (Bosco et al, 1982, Cavagna, 1977) The extent to

which these factors enhance jump height are dependant on elements of the

neuromuscular capacity, such as the capacity to control and utilise high eccentric

loads, coupling time between the eccentric and concentric phase and the ability to

store and utilise elastic energy

The essence of strength resistance training is to enable the muscles to release more

energy Assuming the distance over which the muscles shorten and the duration of

the concentric phase remain the same or reduce, the only way the muscles can release

more energy is if they increase the ability to produce a greater power output (Bobbert,

1990) In order to increase the power output capacity of the muscles an overload must

be induced This implies that exercises chosen must result in the muscles producing a

higher mechanical output (higher forces and power) than during the CMJ

59

Adaptations to the neuromuscular system and resulting improvements in the

performance are specific to the form of training employed Due to the specificity of

the adaptations of the neuromuscular system the training intervention employed must

be a close match to the CMJ This match includes the muscle groups used, the

movement pattern employed, the ROM the joints are brought through, the velocity of

contraction and the type of muscle action employed (Fry and Newton, 2002)

Additionally, the emphases placed at different points of the movement may need to be

similar to the CMJ For example the joint angles where peak moment occurs may

need to be similar between the chosen exercise and the CMJ

2 4 1 Training methods to improve neuromuscular capacity

Several forms of neuromuscular training have been employed to enhance CMJ

performance via the enhancement of some if not all of the above components These

include heavy resistance training (Blattner and Noble, 1979, Toumi et al, 2001),

power training (Plisk, 2001), ballistic training (Hunter and Marshall, 2002, Hakkmen

et al, 1985) and plyometric training (Blattner and Noble, 1979, Brown et al, 1986,

Matavuh et al, 2001) or a combination of the above (Clutch et al, 1983, Hunter and

Marshall, 2002)

Heavy resistance training involves moving a heavy load (close to the athletes single

repetition maximum (1 RM)) through a given range at relatively slow velocities Due

to the velocity specificity of training effect, heavy resistance training may mainly be

beneficial at the start of the concentric phase where the movement is slower, with a

lesser effect at higher velocities (Newton, 1998) For activities such as vertical

jumping where the time available to apply force is limited, the muscles must exert as

much force a possible in a short period of time Therefore, a high rate of force

development (RFD) is desired While heavy resistance strength training may enhance

maximum force it may come at the expense of a decrease in rate of force development

(fig 2 4) (Kraemer and Newton, 1994, Kerin, 2002)

In contrast to heavy resistance training, power training or “explosive” resistance

training involves moving a lighter load but at higher velocities (Fry and Newton,

60

2002) This has been proposed to result in improvements in both RFD and peak

force, shifting the force-time curve up and to the left However, changes at the high

force portion are smaller than those resulting from heavy resistance training but may

enable faster development of forces in the early portion of the movement These

specific changes may be due to explosive resistance training causing an increase in

the amount of neural input This increase is due to rapid voluntary and/or reflex

induced enhancement during a short period of time This is evident in the shift in

EMG-time curves (Fry and Newton, 2002)

In both heavy resistance and explosive power training, the load is decelerated towards

the end of the range of joint extension In the traditional bench press the bar is

decelerating for 24% of the concentric phase for maximum loads and 52% for lighter

loads (Newton, 1998) The problem of deceleration can be overcome if the athlete

throws the weight or jumps at the end of the extension phase This has been termed

“ballistic” resistance training (Newton, 1998) Ballistic training for jumping may take

the form of a movement from a squatting position rapidly lifting a weight so as the

feet leave the ground as the body becomes upright or jumping with a weighted vest

(Hunter and Marshall, 2002) Ballistic training may present problems of high forces

upon landing or when catching the falling weight

61

Another aspect of strength for jumpers may be elastic or reactive strength (Moura and

Moura, 2001) Reactive strength can be defined as the ability to utilise the stretching

of the muscle during the eccentric phase and the ability to change from an eccentric to

a concentric contraction (Young, 1995) Vertical jump performance has been shown

to respond to training which involves performing a SSC movement with a greater

eccentric load and a more rapid stretch than which they are accustomed to (Kerin,

2002) These activities, termed plyometncs are thought to develop the capability for

enhancement of muscular power production and strengthen the neuromuscular system

due to the virtue of greater forces imposed upon the system (Lees and Fahmi, 1994)

One of the most popular plyometric drills is drop jumping (DJ), which involves

falling from a raised platform and upon landing immediately performing a vertical

jump (Bobbert, 1990) The dynamic characteristics and coordination of drop jumping

are thought to provide qualitative specificity to the CMJ (Bobbert, 1990, Kiren, 2002,

Young et al, 1999) Additionally, drop jump training purportedly enhances the ability

to utilise the SSC and increases the overall neural stimulation The delay between the

eccentric and concentric contractions is due to a electromechanical delay in the

muscles and is referred to as the “amortization” (Toumi et al, 2001) or “coupling”

phase (Bosco et al, 1981) Drop jumping has been proposed to train the

neuromuscular system to make a rapid transition from eccentric to concentric

contractions, reducing the coupling time and allows greater utilisation of the SSC

(Kerin, 2002)

2 4 2 Changes in kinetic parameters m drop jumps

The enhancement in jump height following a training program that includes drop

jumps has been suggested to be due to an improvement in the mechanical output of

the muscles, triggered by an overload of the muscles during drop jumping (Bobbert et

al, 1987b) A number of studies have reported greater jump height in the DJ

compared to the CMJ (Asmussen and Bonde-Petersen, 1974, Lees and Fahmi, 1995)

but few studies have examined the difference in the kinetics that may have caused the

increase in height achieved (Bobbert et al, 1986a, Bobbert et al, 1987a, Lees and

Fahmi, 1994, Voigt et al, 1995)

62

2 4 2 1 Drop jump technique

The magnitude of the enhancement in the jump kinetics in the DJ over the CMJ has

been found to be influenced by the drop jump technique employed (Bobbert et al,

1986a) Bobbert et al (1986a) asked subjects to perform drop jumps and observed

that some subjects chose a jumping strategy that employed a movement amplitude of

the BCOM comparable to that utilised during the CMJ The duration of the

concentric phase lasted longer than 260ms (mean CMJ 280ms), referred to as a

counter drop jump (CDJ) Others individuals preferred a movement with a small

amplitude and a positive phase lasting less than 200ms, referred to as the bounce drop

jump (BDJ) The choice of the DJ technique seemed arbitrary and was not related to

anthropometrical variables The magnitude of kinematics and kinetics reported by

Bobbert et al (1986a) and (Bobbert et al, 1987a) where individuals were directed to

perform a CMJ and both the CDJ and the BDJ are outlined at a whole body level in

table 2 21 and at a segmental level in table 2 22 and table 2 23

Table 2 21 Comparison of whole body concentric phase parameters between CMJ and DJ for the two groups in the study by Bobbert et al (1986a) study and the three conditions in Bobbert et al (1987a)_____ _____________________________________

Bobbert et al (1986a) counter group bounce group

Bobbert et al (1987a)

CMJ DJ CMJ DJ CMJ CDJ BDJMovement amplitude (m) 0 35 0 33 033 021* 0 37 0 25* 0 13 * oPhase duration (s) 0 28 0 28 0 28 0 17* 0 29 021* 0 13 *ovGRF at start of phase (N) 1792 1941 1613 3052* 2012 2612* 4015*oMean phase vGRF (N) 1555 1562 1531 2082* 1715 1918* 2561*oNote * value differs from the CMJ

o value differs from CDJ

63

Table 2 22 Kinematic and kinetic output of CMJ and DJ (Bobbert et al, 1986a)Counter group Bounce group

CMJ DJ CMJ DJHip 1 21 1 38 1 44 2 06*

Angle at JR Knee 1 34 132 1 48 1 76*(rad) Ankle 1 34 1 39* 1 3 1 32

Hip 343 351 269 270Moment at JR Knee 247 308 229 407 *(Nm) Ankle 236 249 193 420 *

Hip 366 368 344 305Peak Moment Knee 279 331 276 414*(Nm) Ankle 266 279 246 440 *

Hip 1551 1338 1405 1203Peak Power Knee 1657 1762 1481 1936*(W) Ankle 1886 1776 1829 2425

Hip 234 187 * 189 84 *Work Knee 193 215 163 146(J) Ankle 171 157 158 203 *Note * value differs from the CMJ

For the individuals that utilised the CDJ technique, the amplitude of movement and

duration of concentric phase did not differ to that of the CMJ resulting in similar

kinematics, with the exception of less dorsi-flexion and a reduced but not statistically

significant hip flexion This resulted in less hip work done, the only kinetic difference

observed In contrast, the BDJ was characterised by reduced amplitude of movement

and a shorter duration of the concentric phase This resulted in a greater vGRF at the

start of the concentric phase and higher mean force but less work done due to the

reduced amplitude of movement The reduction in the amplitude is attributed to a

reduction in knee and hip flexion As less time was available to decelerate the BCOM

greater vGRF were evident at the start of the concentric phase, which were manifested

in greater knee and ankle joint moments at joint reversal Both average moment and

peak moment at the knee and ankle joints were greater than during the CMJ The

knee joint was the only joint that exhibited an increase in peak joint power during the

BDJ compared to the CMJ, while a large but non-significant increase was evident at

the ankle joint Peak hip joint power was also reduced

In light of DJ technique altering the kinetics of the jump, Bobbert et al (1987a)

conducted a more controlled study where subjects were asked to perform a series of

64

jumps from 20cm utilising both the CDJ and the BDJ, which were compared to the

CMJ Kinematic and kinetic variables reported by Bobbert et al (1987a) are outlined

in tables 2 21 for whole body parameters and table 2 23 for segmental parameters

Three points that must be noted when comparisons are made with the previous study

relating to technique Firstly, drop height was reduced by 20cm (see section 2 2 7 for

more detailed discussion on changes with drop height) Secondly, given that trained

volleyball players were used as opposed to handball players, training specificity may

have lead to different responses to drop jumping The skill level appears to be greater

in the volleyball group, evident by a 5cm greater CMJ height on average Finally, a

shorter duration of the concentric phase and amplitude of movement of the BCOM

was utilised in both forms of drop jumping compared to the CDJ in the study by

Bobbert et al (1986a) The mean duration of the CDJ (210±30ms) approached the

criteria for the BDJ (<200ms) set out in the previous study It appears both forms of

drop jumping exhibit characteristics of the BDJ in the previous study, which must be

taken into account when examining the response to the drop jumping stimulus on the

kinetic parameters The CDJ m the study by Bobbert et al (1986a) did not differ from

the CMJ with respect to the amplitude of movement of the BCOM or duration of the

concentric phase, whereas the CDJ in the study by Bobbert et al (1987a) did and for

this reason should be viewed as larger amplitude BDJ

65

Table 2 23 Mean kinematic and kinetic variables from CMJ and DJ (20cm)

(from Bobbert et al, 1987a)CMJ CDJ BDJ

Hip 1 23 1 74 * 2 29 *oAngle at JR Knee 1 40 1 51 * 1 93 *o(rad) Ankle 1 23 1 25 1 26

Hip 403 326 287 *Moment at JR Knee 314 473 * 546 *o(Nm) Ankle 263 349 * 586 *o

Hip 422 367 * 310 * oPeak Moment Knee 366 488 * 558 *o(Nm) Ankle 310 361 * 602 *o

Hip 1524 1255 1165Peak Power Knee 2549 2796 3004 *o(W) Ankle 2449 2482 4529 *oNote * value differs from the CMJ

o value differs from CDJ

In Bobbert et al (1987a) for both forms of DJ the amplitude of movement of the

BCOM, the duration of both the eccentric and concentric phases and the maximum

joint angle attained by the hip and the knee were less than during those of the CMJ,

and the changes were greater in the BDJ Increases in knee and ankle joint moments

at joint reversal and peak values were evident in both forms of drop jumps, consistent

with the results for the BDJ found by Bobbert et al (1986a) Additionally, a lower

peak hip joint moment was present in both forms of drop jumps and a reduced hip

joint moment at joint reversal was evident in the BDJ, but the change experienced in

the CDJ was not statistically significant (p>0 05) In contrast, peak joint power was

not significantly different to that of the CMJ for the CDJ but was significantly greater

for the knee and ankle joints in the BDJ

While Bobbert and his colleagues identified two distinct techniques, when individuals

are asked to perform an unrestricted DJ for maximum jump height, they chose a

technique on a continuum from a jump with a small amplitude and short ground

contact time to a jump at the other end of the spectrum (Hunter and Marshall, 2002)

It has been shown that variance in the duration of the concentric phase of the CMJ

also exists (Jane et al, 1989, van Soest et al, 1985) The use of absolute cut-off

durations for the categorisation of jump strategy seems inappropriate Categorisation

based on the change in a jump parameter between jump conditions, such as amplitude

66

of movement or duration of a phase may provide a more robust mechanism As a DJ

is an example of a SSC movement, categorisation based on the duration of the

eccentric phase may prove more appropriate as it may provide a better representation

of the characteristics of the stretch applied, while the amplitude of movement

provides another means

2 4 2 2 Drop jump height

The enhancement m mechanical output over that of the CMJ in jumps similar to the

BDJ, outlined by Bobbert et al (1986a) is due to factors relating to the SSC, which

increase with the velocity of the stretch of the active muscles in the eccentric phase

and decrease with the coupling phase duration The velocity of stretch the muscle

experiences is dependent on the peak negative velocity of the BCOM, which may be

varied by increasing the drop height preceding the jump (Bobbert et al, 1987b)

Asmussen and Bonde-Petersen (1974) compared the effect of dropping from three

different heights (0 233m, 0 404m and 0 69m) to a CMJ and examined the effect on

the jump height achieved and positive phase energy produced They found jump

height increased from that attained in the CMJ following a drop from 0 233m and

increased further following a drop from 0 404m However, following a drop from

0 69m the jump height did not statistically differ from the height attained in the CMJ

At an individual subject level, drop jumping did not result in a greater jump height

than that of the CMJ for two individuals, while six individuals continued to increase

jump height up to a drop from 0 69m Lees and Fahmi (1995) also found a greater

jump height for the DJ than the CMJ when they examined drop heights of 0 12m,

0 24m, 0 36m, 0 46m, 0 58m, and 0 68m, but not for all drop heights The greatest

height achieved was from the lowest drop height of 0 12m and jump height

diminished as the drop height increased Heights above 0 46m resulted in lower jump

heights being achieved than in the CMJ Voigt et al (1995) found no difference in

jump height following a drop from 0 3m compared to the CMJ, and a decrease when

drop height increased to 0 6m and again to 0 9m In contrast to these findings, many

studies have found no difference in jump height following a drop from various heights

(Bedi et al, 1987, Bobbert et al, 1987b) Bedi et al (1987) found no difference m

67

jump height achieved following drops of between 0 25m and 0 85m at 0 lm

increments, while Bobbert et al (1987b) found no difference in jump height between

drops of 0 2m, 0 4m and 0 6m For both studies no comparison was made with a

CMJ

Selection of an optimum drop height has traditionally been based on which drop

height allowed the greatest jump height achieved (Asmussen and Bonde-Petersen,

1974, Bedi et al, 1987, Young et al, 1999b) In light of the findings by Bobbert et al

(1986a) that a drop jump technique utilising a large amplitude of movement may

benefit jump height and another technique with a reduced amplitude may benefit the

overload of mechanical output of the muscles, selection of drop height based on jump

height achieved may not be the best option Young et al (1999b) examined drop

heights of 0 3m, 0 45m, 0 6m and 0 75m and found that jump height achieved was

greatest at 0 6m but resulted in the second longest contact time However, the lowest

drop height (0 3m) resulted in the best reactive strength (jump height divided by

contact time) It has been suggested that the larger the reactive strength load the

greater the mechanical overload on the muscles (Young et al, 1999b), however, no

measurement of joint kinetics were recorded to support this view Few studies have

reported changes in kinetics following drops from different heights (Bobbert et al,

1987b, Lees and Fahmi, 1994, Voigt et al, 1995) Lees and Fahmi (1994) found that

the lowest drop height examined (0 12m) resulted in the greatest combined

enhancement based on the height achieved, the peak vGRF, the peak vertical velocity

of the BCOM and the peak whole body power Average mechanical power was found

to be enhanced during DJ in comparison to CMJ (Voigt et al, 1995) following a drop

of 0 3m and 0 6m, which were both greater than the average mechanical power in

jumps from 0 9m Optimal drop height is likely to be dependant on the current

neuromuscular capacity and past experiences of an individual From an evolutionary

sense the human body may be better tuned neuromuscularly to impacts originating

from lower heights, akin to running, hopping and skipping (Lees and Fahmi, 1994)

There is no a priori reason why the neuromuscular system would respond more

favourably to greater rather than lesser drop heights Lees and Fahmi (1994)

concluded that if an optimum drop height exists as a natural biomechanical feature of

human neuromuscular system, it is more likely to be lower rather than higher

68

The kinematics of the jump has been found to differ between drop heights (Bobbert et

al, 1987a, Lees and Fahmi, 1994) Bobbert et al (1987b) found no statistical

difference in the duration of the eccentric phase between drop heights but the duration

of the concentric phase took longer following a drop of 0 6m than it did following

0 4m Much of this could be attributed to a reduced amplitude of movement of the

BCOM following a drop of 0 4m (0 03m, p <0 05), brought about by a reduced ROM

of the knee joint (0 1 lrad, p <0 05) Reduced amplitude of movement of the BCOM

(0 04m) was also observed by Lees and Fahmi (1994) but only at the lowest drop

height of 0 12m, and increased thereafter possibly to absorb the increase m vGRF

upon landing from the greater drop heights This was achieved by increasing the

ROM of the knee and hip joints

At whole body kinetic level Bobbert et al (1987b) found no difference in the vGRF at

the start of the concentric phase between drop heights However, peak vGRF was

statistically greater following a drop of 0 4m than 0 2m, and greater again following a

drop of 0 6m However, these values appear to be the first impact peak observed and

would be unlikely to be related to jump performance The net impulse during the

eccentric phase was found to increase with drop height (DJ20 1 97 N s kg 1 < DJ40

2 47 N s kg 1 < DJ60 3 09 N s kg \ p < 0 05) but no statistical difference was

observed during the concentric phase

When examining the joint moment at reversal, peak joint moment and peak joint

power, Bobbert et al (1987b) only found peak ankle joint moment and peak ankle

joint power to be statistically different between drop heights Peak ankle joint

moment was on average 56N greater following a drop of 0 4m compared to 0 6m and

peak ankle joint power was on average 184W greater following a drop of 0 4m

compared to 0 6m However, while not statistically significant both peak ankle joint

moment and power following a drop of 0 4m was greater than that developed

following a drop of 0 2m At both the knee and hip joints no statistically significant

differences were observed between drop heights However, the mean knee joint

moment at joint reversal, peak knee joint moment and knee joint power were greater

following a drop of 0 4m but not statistically different compared 0 2m and 0 6m

possibly be due to greater variability observed at the knee joint Likewise a greater

but not statistically significant ankle joint moment at joint reversal and peak value

69

was observed after a drop of 0 4m compared to 0 2m and 0 6m The greater mean

differences and variability observed m these measures suggest there may have been an

enhancement for some individuals However, as individual data was not reported it is

not possible to make any conclusions on this matter

The enhancement of kinetic variables following a drop of 0 4m was matched by

reduced but not statistically significant amplitude of movement of the BCOM and

duration of both the eccentric and concentric phases at that drop height This is

consistent with the finding by Bobbert et al (1986a) regarding drop jump technique

It is possible that the other two heights (0 2m and 0 6m) did not either provide enough

stimulus or were too excessive to allow rapid deceleration of the BCOM following

landing, possibly requiring a longer duration and amplitude to dissipate the excessive

vGRF upon landing It must be noted that the subjects performed all the jumps in

bare feet and it is possible the vGRF experienced was too great to accommodate

Lees and Fahmi (1994) found subjects were reluctant to contact the force platform

vigorously with bare feet At greater impact forces the human body is obliged to

protect it’s structures and as a result may lose the ability to recover energy stored in

these structure (Less and Fahmi, 1994) Comparisons between drop heights between

studies may be misleading due to differing techniques imposing a greater stretch load

for comparable drop heights (Young et al, 1999)

2 4 3 Drop jump training studies

Some studies have found that drop jump training enhances vertical jump height in the

CMJ (Blatter and Noble, 1979, Brown et al, 1986, Clutch et al, 1983, Gehri et al,

1998, Matavulj et al, 2001) A summary of results of DJ training is outlined in table

2 24 While a degree of enhancement was observed in all studies, enhancements were

not statistically significant for all Brown et al (1986) only found a statistical

significant enhancement for jumps involving an arm swing, while a 5 5cm

enhancement was observed in jumps without the use of arms, the enhancement did not

prove to be statistically different The greater variability in jumps without the arms

may have been responsible for the lack of statistical significance Clutch et al (1983)

70

found a significant increase m jump height for untrained subjects, but found no

significant increase in skilled jumpers

Table 2 24 Effect of drop jump training on CMJ performanceStudy number of

subiectsTraining Drop height ACMJ height Statistical

significance

Blatter & Noble (1979)

11 DJ12 isokinetic 15 control

(3x10 DJ) x 3 sessions x8 weeks 0 86m 2 1 cm yes

Brown et al (1986)

13 DJ 13 control

(3 x 10 DJ) x 2 sessions xl2 weeks 0 45m 5 5cm no A

12 subjects CMJ, DJ30, DJ (75, 110) 0 30m 3 35cm yes

Clutch et al 2 sessions x 4 weeks each condition 0 75m & 1 lm 2 97cm yes

(1983) Skilled 8 (4x10 DJ) x 2 sessions xl6 weeks 0 75m & 1 lm 3 73cm noUnskilled 8 (4 xlO DJ) x 2 sessions xl6 weeks 0 75m & 1 lm 3 21cm yes

Gehri et al (1998)

11 DJ7 CMJ 10 control

see note * below 0 40m 2 13cm yes

DJ 50 (3 x 10 DJ) x 3 sessions x6 weeks 0 50m 4 8cm yes

Matavulj et al (2001)

DJ 100 Control

(3 x 10 DJ) x 3 sessions x6 weeks 1 00m 5 6cm yes

Note A jumps without the use o f arm were not significantly enhanced with DJ training but jumps with the use o f the arms were

* 2 sessions per week for 12 weeks, 2 x 8 jumps for first 2 weeks, then 4 x 8 jumps

The differences between studies and lack of response in others may have been due to

differences in the way DJs were performed It has been shown that DJ technique

influences the overloading of joint kinetics (Bobbert et al, 1987a) While some of the

studies instructed individuals to jump as soon as possible after landing (Blatter and

Noble, 1979, Matavulj et al, 2001, Young et al, 1999b), no instruction was given by

Brown et al (1986) In light of the findings of Bobbert et al (1986a) where some

individuals utilise a technique with an amplitude of the movement of the BCOM

comparable to the CMJ which did not overload joint kinetics, it is possible that the

technique of some of the individuals within the Brown et al (1986) study may have

been the reason no significant enhancement in jump height was observed

In light of the potential differences in training effect due to DJ technique Young et al

(1999b) examined two DJ techniques during a six week DJ training program The

aim of the first technique was to maximise rebound height (DJ-H) and the second

technique aimed to achieve the best combination of rebound height and minimum

contact time (DJ-H/t) Thirty five subjects training for six weeks utilising the DJ-H

technique and thirty five utilising the DJ-H/t technique along with a control group of

71

thirty five who did not undertake any form of jump training were studied After six

weeks of training CMJ height increased by 0 9cm in the DJ-H/t group, however, this

enhancement was not found to differ in either the DJ-H or the control group Due to

the high number of subjects dropping out of the study in this group the low number of

subjects may be partly responsible for lack of statistical significance However, the

enhancement in CMJ height achieved is much lower than other studies (Blatter and

Noble, 1979, Brown et al 1986, Clutch et al, 1983, Gehn et al, 1998) These studies

did have longer training programs but, the amount of jumps is comparable to Matavulj

et al (2001) which achieved an enhancement of 4 8cm and 5 6cm for DJ from 0 5m

and lm, respectively It is possible that the greater drop height used provided a

greater overload along with the relatively young age of the subjects enabled the

greater enhancement observed by Matavulj et al (2001) Additionally, the CMJ used

to test enhancement due to training allowed the use of the arms while in the DJ

training employed the arms were restricted The only significant enhancement was a

greater reactive strength (rebound height/contact time) for the DJ-H/t group, which

supports the specificity of training When neuromuscular capacity is altered the

coordination pattern needs to be re-optimised (Bobbert and Van Soest, 1994, Nagano

and Gerritsen, 2001), it is possible that the coordination pattern for the CMJ utilising

the arm swing post training may have been at a sub-optimised level for the enhanced

neuromuscular capacity A possible reason for the lack of a significant enhancement

in the DJ-H group is that the drop height/technique combination was not enough to

induce an overload in the jump kinetics While drop heights used for training where

not stated, heights chosen were those that maximised rebound height while the height

chosen for the DJ-H/t group maximised the best combination of rebound height and

minimum contact time From the data reported for the DJ-H/t group it appears

different drop heights may have been used in the training between groups

72

Methodology

73

Two forms of analysis to identify factors that correlate with jump performance were

undertaken, group analysis (inter-subject) based on differences between individuals

and individual subject analysis (intra-subject) based on differences within repetitions

of an individual’s own movement The group analysis was further divided into two

approaches found in the literature for selecting a representative value for each subject

A single value per subject was selected two ways, the mean value of the 15 jumps

undertaken (G m) and the best jump of the 15 (G b) Comparison of these three

approaches was made

31 Subjects

Eighteen male subjects (age 23 5±5 3 years and mass 75 2±11kg), who were not

currently involved in any form of jump training, participated in the study Ethical

approval was received from Dublin City University Information regarding testing

was given to all subjects and informed consent was received from all subjects prior to

testing All subjects were injury free at the time of the test

3 2 Experimental protocols

Each subject performed three categories of jumps, differing in the amount of eccentric

loading the counter movement jump (CMJ) and drop jumps (DJ) from two different

heights (0 3m and 0 5m) During the CMJ, the subject lowered their body’s centre of

mass (BCOM) from a standing upright position by flexing of the lower extremity

joints (see section 2 2 for more detailed description) Increased eccentric loading was

introduced in the DJ by increasing the amount the velocity of the BCOM had to

decrease during the eccentric phase This was achieved by stepping down from boxes

whos heights were 0 3m (DJ30) and 0 5m (DJ50) Subjects were instructed to step off

the boxes with their dominate foot and land with both feet simultaneously contacting

a separate force plate These heights were selected as they were evident in the

literature for novice jumpers (Brown et al, 1986, Gehn et al, 1998) Subjects attended

on two occasions, the first to familiarise themselves with the protocols, the second

involved the collection of data

74

Figure 3 1 Diagram of experimental set-up

Subjects were instructed to jump maximally in all jumps and to jump immediately

upon landing during the DJ No additional instructions were given to insure self-

selection of technique and elimination of any investor-induced bias into the

experiment In all jumps the subject placed their hands on their hips to reduce the use

of arms allowing the jump height to be predominately due to the contribution of the

leg muscle groups (Bobbert et al, 1986a) Feet were kept parallel with the x-axis of

the force platform, restricting motion to the sagittal plane as much as possible Jumps

were accepted for analysis when both the subject and the investigator deemed that

effort was maximal, take-off and landing occurred in approximately the same position

and balance was maintained

Each subject performed 15 acceptable trials under each jump condition This number

of trials was found by Moran (1998) using sequential estimation techniques (Hamill

and McNiven, 1990) to allow determination of representative jump kinematic and

kinetic data The order of each jump conditions were block randomised for each

subject to eliminate any condition-sequence interaction A 30 second rest between

CMJs and 60 seconds between DJs, and at least 3 minutes between conditions was

imposed to reduce the likelihood of fatigue The trial number was recorded to check

75

for sampling specific trends in the jump height achieved Subjects wore brief shorts

and their own sports shoes

3 3 Data Acquisition

Locations of anatomical landmarks were marked on the skin to enable markers to be

accurately replaced in the original location in the event of displacement during

testing Five reflective spherical skin mounted markers were place on anatomical

landmarks of both sides of the body - fifth metatarsal joint, lateral malleolus, lateral

femoral epicondyle of the knee, the most prominent protuberance of the greater

trochanter and the glenohumeral joint indicating the joint centres of the toe, ankle,

knee, hip and shoulder, respectively (Bobbert et al, 1986) Additionally, a sixth

marker was placed on the heel, level with the toe marker (Robertson and Fleming,

1987) Markers were fixed to the skin using medical tape

A VICON motion analysis (VICON 512 M, Oxford Metrics Ltd, England) system

was used in conjunction with an AMTI force platform mounted in the ground (BP-

600900, AMTI, MA, USA) and AMTI amplifier VICON software controlled

simultaneous sampling of motion and force data at 250Hz Eight cameras placed

evenly around the sampling area emitted infrared light from diode stroboscopes in

each camera, which was reflected back to the cameras by the reflective spherical skin

markers Two-dimensional co-ordinate data was calculated for each camera and

subsequently three dimensional co-ordinate data for the captured motion was

calculated by direct linear transformation (VICON v4 6, Oxford Metrics Ltd,

England)

Raw co-ordinate data and force data were exported to Excel and subsequently applied

to a number of specially designed in-house computer programs developed by the

author The data was filtered using a recursive second-order low pass butterworth

digital filter (Winter, 1990) The once filtered data was filtered again, but in the

reverse direction of time, so as to introduce an equal and opposite phase lead so as to

result in a net phase shift of zero (Winter, 1990) The force plate data was filtered at

70Hz (Moran, 1998) The marker positional data was filtered at different values

(table 3 1), found using residual analysis to minimise the root mean square (RMS) of

76

the difference between the filtered and unfiltered data over a range of cut-off

frequencies (Moran, 1998) The same cut-off frequency for the toe marker was used

for the heel marker as both were not subject to skin movement

Table 3 1 Cut off frequencies of each joint marker (Moran, 1998)Toe Heel Ankle Knee Hip Shoulder

CMJ 6 62 6 62 7 52 921 8 50 6 64DJ 6 61 6 61 7 48 9 14 8 38 6 41

3 4 Data analysis

The body was modelled as a rigid-body, planar system consisting of four segments

linked by fnctionless hinge joints The four-segment model of the body has been

used in numerous jumping experiments (Aragon-Vargas & Gross, 1997, Hubley and

Wells, 1983, Jaric et al, 1989) The four segments were the foot, shank, thigh and

head-arms-trunk (HAT) separated by the ankle, knee and hip joints, respectively The

lower legs were conceptionahsed as a ‘single equivalent muscle’ model (Robertson

and Fleming, 1987), where the three joints were viewed as having six ‘muscles’

arranged in pairs crossing each joint, one of each pair representing tissues that act as

extensors and the others as flexors

The eccentric and concentric phases of the jump were defined with respect to the

vertical velocity of the BCOM the eccentric phase started with the initiation of

negative vertical velocity of the BCOM and ended when the velocity reached zero and

the BCOM was at a minimum height (Hudson, 1988), the concentric phase began the

instant that the BCOM obtained positive vertical velocity and ended when the toes

lost contact with the force platform

77

The vertical height achieved in the jump was calculated as the vertical difference

between the BCOM when standing and at the apex of the jump (Bobbert et al, 1987a)

The vertical height of the BCOM (Y bcom ) was calculated as

Ybcom = £ (/?; *YCOM)Equation 3 1

WhereR, was the ratio of segment weight to whole body weight (table 3 1, pp56-57, Winter 1990)YCOM, was the vertical height of the COM of segment i

Figure 3 2 Diagram for body segments and angle conventions

Segment angles were calculated in an anti-clockwise direction from the right

horizontal with the distal end point of the segment as the origin The segments angles

were defined as 0foot, Qshank, Gthigh, Ghat (for the upper body) (Figure 3 2) The joint

angles were calculated as the angle between adjacent segments

Oankle — 71 — Oshank “1* Ofoot Equation 3 2

Oknee — 7 t — Oshank "1" Othigh Equation 3 3

Qhip = 71 — O h a t + Gthigh Equation 3 4

Shouldej

Knee Kneeangle

Foot

78

Joint and segment kinetics were calculated by inverse dynamics from kinematic

(Johnson and Buckley, 2001, Winter, 1990), ground reaction force data and

anthropometric data (table 3 1, pp56-57, Winter 1990) Counter-clockwise moments

acting on the segments distal to the joint were considered to be positive Joint

reaction forces and moments were calculated as follows

Fxp = ( Mass * Ax) + Fxd Equation 3 5

Fyp = {Mass * A y ) + F yd+ (m * g ) Equation 3 6

WhereFxp, Fyp = proximal joint reaction force in the x or y direction Fxd, Fyd = distal joint reaction force in the x or y direction Ax, Ay = acceleration in x or y direction m = mass of segment g = acceleration due to gravity

Fxp

d2

d1

I----------------1-------------- 1d3 d4

Figure 3 3 Free body diagram for generic body segment

M P = Md + (Fxd * d \ ) + {Fxp* d l ) - t Fyd * d 3) - (FyP * d4) + l a Equation 3 7

WhereMp = joint moment at proximal Md = joint moment at distal end I = moment of inertia about the segment centre of mass a = segment angular acceleration

79

Hip extensor, knee extensor and ankle plantar flexor moments were defined as

positive (Bobbert et al, 1987a) Net joint muscle power for each joint was calculated

as the product of the net muscle moment and the joint angular velocity (Fukashiro and Komi, 1987)

Work done by the muscles during each phase was equal to the integral of power with

respect to time (van Ingen Schenau et al, 1985) Integration was performed using the trapezium rule with work calculated for positive and negative phases separately

3 5 Variable selection

Kinematic and kinetic variables were evaluated in terms of both magnitude and

timing The variables selected for analysis were sub-divided into five main phasesi Kinematics and kinetics during the eccentric phase

n Kinematics and kinetics at the start of the concentric phasein Kinematics and kinetics during the concentric phaseiv Body position at take-offv Rise in the BCOM after take-off

Additionally, the duration of phases i and 111 (above) and the delay between the

eccentric and concentric phases, defined as ‘coupling’ time (Bosco and Komi, 1979),

were analysed Kinetic variables were normalised for body mass to control for differences in body weight

Kinematics and kinetics during the eccentric phase

The actions of the muscles during the eccentric phase strongly influences muscle

actions during the concentric phase (Bosco et al, 1981, Cavagna et al, 1965) The

variables selected for analysis were Peak negative vertical velocity of the BCOM,

peak whole body power, peak joint angular velocity, total and individual joint work

P = M jCOj Equation 3 8

Equation 3 9

80

done and the percentage of total work done at each joint (Bobbert et al, 1987b,

Harman et al, 1990)

Kinematics and kinetics at the start of the concentric phase

Kinematics and kinetics at the start of the concentric phase have been shown to affect

the kinetics during the concentric phase (Asmussen and Blonde-Petrsen, 1974, Bosco and Komi, 1979) The variables selected for analysis were amplitude of movement of the BCOM, minimum joint angle (joint reversal), force (vGRF) at start of positive

phase, the joint moment at joint reversal (Aragon-Vargas & Gross, 1997, Bobbert et

al, 1987a, Bosco et al, 1981, Jane et al, 1989) and coupling time (the time taken for

the joint to rotate from one degree prior to joint reversal to one degree after joint

reversal) (Bosco et al, 1981)

Kinematics and kinetics during the positive phase

The height the BCOM attains after take-off is dependent primarily on the vertical

velocity of the BCOM at take-off Kinematic and kinetic factors which directly and

indirectly affect this were examined peak vGRF, peak joint moment, total and

individual joint peak power, total and individual joint work done and the percentage

of total work done by each joint (Aragon-Vargas and Gross, 1997, Bobbert et al,

1987a, Fukashiro and Komi, 1987, Robertson and Fleming, 1987, Rodano and

Roberto, 2002)

Body position at take-off

The height the BCOM attains post take-off is dependent on the kinetic and potential energy at take-off (Bobbert and van Ingen Schenau, 1988) The potential energy is

determined by how high the BCOM is located at take-off, therefore the vertical height difference of BCOM at take-off from that of standing was examined

Rise in the BCOM after take-offJump height was defined as the difference between the peak height the BCOM

attained at the apex of the jump and that at standing (Bobbert et al, 1987a) This was

taken as the measure ofjump performance

81

Coordination is a major factor in proficient execution of a motor task and refers to the

timing and sequence of segmental movements Coordination was analysed at the joint

level by examining the time delay between key events of adjacent joint pairings hip

and knee, knee and ankle The following variables were examined initiation ofjoint extension (Rodacki et al, 2002), peak joint angular velocity (Jensen et al, 1994), peak

joint moment and peak joint power (Bobbert and van Ingen Schenau, 1988) Absolute

timing difference between events was taken In addition to negate the effect of the

total duration of the movement, timing delays were also examined as a proportion of

total concentric phase duration (relative timing) (Rodacki et al, 2001)

Figure 3 4 Measures of rate of force development

The rate of force development (RFD) was calculated as the rate of change in the

magnitude ofjoint moment or vGRF over selected time intervals The rate of power development was calculated for individual joints as the increase in joint power in the first 60ms of the concentric phase The selected intervals (Figure 3 4) were -

• From joint reversal (or start of concentric phase) to the instant of take-off (A and E)

• From the minimum vGRF to joint reversal (or the start of concentric phase) (B and F)

• From the instance of minimum vGRF to peak moment (or peak vGRF) (C and G)

• From the instance of minimum vGRF to 50% peak moment (or peak vGRF) (D1 and HI)

82

• From 50% peak moment/vGRF to peak moment (or peak vGRF) (D2 and H2)

Since isometric tests examine the RFD without eccentric loading, it was of interest to

determine if a relationship exists between jump height and neuromuscular output in

the concentric phase only in the CMJ From JR to peak force is the only portion of

the jump where force is developed by solely a concentric contraction However, the

interval from JR to peak joint moment (or vGRF) was not included because for many

subject these two events occurred simultaneously or the peak occurred prior to JR

2 6 Statistical analysis

Descriptive statistics (mean magnitude and variance) were calculated for the jump

height achieved and each biomechanical jump parameter at both a group level (G b

and G m) and individual subject level Pearson product moment correlations were

performed between the biomechanical parameters and the jump height achieved An

a = 0 05 level was adopted for statistical significance Bivariate regression techniques

were applied to calculate the slope of the relationship to jump mechanical parameters

found to be significantly correlated with jump height achieved The residuals from the bivariate analysis were plotted against the predicted values to verify that the basic

assumptions of normality were met The influence of outliners was assessed by visual

observation of plotted values against jump height and in borderline cases using

Cook’s distance, outliers where subsequently omitted from analysis Visual

examination of scatter plots of each variable and jump height was undertaken to

determine weather a linear pattern was present, and was verified by plotting the residuals against the predicted values from the bivariate regression analysis

(Montgomery, 1991) Hypothesis concerning differences between jump conditions were tested using a two-way repeated measures analyses of variance (ANOVA) in the case of group analyse and a one-way repeated measures ANOVA in the case of individual analyse An a = 0 05 level was adopted for statistical significance Where

statistical differences were observed a Tukey’s post-hoc analysis was employed All

statistical analysis was performed using SPSS (version 10)

83

Results

84

The group mean, the inter-subject variability and the mean intra-subject variability for the biomechanical parameters of the CMJ are detailed below Results of correlation

analysis at the group level using both the mean magnitude for each of the 18 subjects

(G m), and the data from each subject’s best performance (G b) are presented In

addition, individual subject correlation analyse utilising all 15 jumps undertaken by

each subject are presented Where no correlation is reported, that parameter was not

found to be correlated with jump height (a = 0 05 significance level The data is

sectionalised in the following phases

(i) the eccentric phase

(11) the transition phase between the eccentric and concentric phases (in) the concentric phase

Differences in jump kinetics between CMJ and DJ from 0 3m and 0 5m will be

outlined to investigate the possible use of drop jumping as a means of stressing

specific neuromuscular parameters for training purposes Time history of selected

joint variables (angle, angular velocity, moment and power) for a CMJ of a representative subject is presented in Figure 4 1

85

joint

Powe

r (W

) Jo

int

Mom

ent

(Nm

) An

gula

r ve

loci

ty

(rad/

s)

Join

t an

gle

(rad

)

3 Ankle Knee Hip

0.5

Figure 4.1 Joint time histories for a representative subject.

4 1 Variability and the relationship with jump performance

The following section outlines the extent to which the kinematic and kinetic variables varied both between subjects (inter-subject) and within repeated individual

performances (intra-subject) Variability is presented in the units of the variable

(standard deviation, SD) and standardised as a percentage of the variable’s mean

(coefficient of variation CV) These are presented along with the overall group

mean Results of bivanate statistical analysis for the relationship between the

magnitude of the kinematic and kinetic parameters and the magnitude of jump height

are also presented All correlations where an increase in jump height was observed

with an increase in the magnitude of a parameter are reported as positive Analysis at

the group level used inter-subject data based on both the mean values (G m) and

values from the best jump (G b) Where no correlation coefficient and level of

significance are reported in a table, this indicates that no significant correlation was

evident (a = 0 05) This gives a visual representation of the distribution of significant

parameters Subjects were ranked according to their mean CMJ jump height (e g

subject 1 greatest mean jump height, subject 18 lowest mean jump height)

Kinetics during the negative phase

Table 4 1 outlines the mean magnitude observed for peak negative velocity of the

BCOM, the duration of the eccentric phase, the peak negative whole body power and

the total negative work done during the eccentric phase Variability was notably

lower at the individual subject level than at the group level, with the exception of

whole body peak power where no notable difference was evident

Table 4 1 Mean and variance values of whole body kinematics and kinetics for the group and average variance for individuals during the eccentric phase_________

Group________________ IndividualMean SD CV Mean SD Mean CV

Peak negative velocity (ms ) -1 03 0 32 -30 8 0 09 -9 3Phase Duration (s) 0 54 0 19 34 8 0 08 15 6Peak Power (W) -19 78 8 03 -40 6 7 30 -39 1Work done (J) -2 45 0 60 -24 5 021 -9 4Note SD Standard deviation

CV Coefficient of variability

87

Table 4 2 below details the correlation coefficient (r) and level of statistical

significance (p) for the relationship between jump height and the peak negative

vertical velocity of the BCOM, the duration of the eccentric phase, the peak negativewhole body power and the total negative work done during eccentric phase

Table 4 2 Correlation (r) and level of significance (p) for the relationship between jump height and whole body kinematics and kinetics during the eccentric phase

Peak velocity Phase duration Peak power Work doner P r P r P r P

Gb 0 52 0 026G m 0 60 0 008 -0 47 0 050 0 58 0010

1 0 82 0 007 0 53 0 0362 0 53 0 0353 0 61 0 0094 0 65 0 007 0 69 0 0035£

0 68 0 00307 " ”0 60 0 036

— - — — — ---------------------- ■ -----------

8 0 57 0 035 -0 67 0 0079 -0 57 0 022101112131415161718 0 84 0 008 -0 58 0 019 0 80 <0 001

Note G b Group data based on the best performance of each individualG m Group data based on the mean values of all 15 jumps for each individual

Peak velocity, phase duration and peak power were all found to be correlated with

jump height at a group level (inter-subject) when the mean values of each subject’s 15

jumps (G m) were analysed, while only peak velocity was correlated at a group level when the best jump by each subject was analysis (G b) In contrast to the group analysis, only three of the 18 subjects had significant correlations between jump height and either peak velocity or phase durations at an individual subject level (mtra-

subject) Peak power was not found to be correlated with jump height for any

individuals Total work done during the eccentric phase did not provide a means of

differentiating between individuals at a group level with respect to mean jump height,

however a correlation was apparent for six subjects at an individual level

88

Table 4 3 outlines the mean values for the peak angular velocity and the total work

done during the eccentric phase for each joint Measures of inter-subject variability

and mean values of intra-subject variability are presented Greater variability was

observed between individuals (inter-subject) compared to within an individuals own

performance (intra-subject) In addition, greater variability between individuals was

observed at the ankle joint compared to the knee and hip joints This also held true at

°the intra-subject level for the work done at the ankle, but peak angular velocity at the

ankle was not seen to be more variable than at the other joints

Table 4 3 Mean and variance values of joint kinematics and kinetics during theeccentric phase for the group and average variance for individuals

Group IndividualMean SD CV Mean SD Mean CV

Ankle peak velocity (rad s ‘) -1 37 0 76 -55 6 0 23 -15 5Knee peak velocity (rad s ') -2 64 0 90 -34 2 0 23 -14 3Hip peak velocity (rad s ]) -3 40 0 86 -25 4 0 34 -105Ankle work done (J kg ) -0 29 0 18 -61 8 0 07 -25 6Knee work done (J kg]) Hip work done (J kg )

-0 91 0 38 -42 5 0 11 -12 8-1 25 0 47 -37 8 0 18 -165

Table 4 4 details the correlation coefficient (r) and level of significance (p) for the

relationship between jump height and the peak angular velocity, and the amount of

negative work done at the ankle, knee and hip joints during the eccentric phase At a

group level only peak hip angular velocity was significantly correlated with jump

height and only when mean values (G m) were employed in the analysis This relationship was also evident at an individual level in four of the 18 subjects While

angular velocity at other joints were not significantly correlated with jump height at a

group level, significant correlations were observed for two and three individuals for the ankle and knee joints, respectively Total negative work done was not correlated

with jump height at the group level for any joint Work done at the ankle was only correlated for one individual, while work done at the knee and hip joints were

correlated with jump height for five and seven individuals, respectively Three of the five individuals that exhibited a correlation between knee negative work done and

jump height had a positive correlation, while six of the seven had a positive

correlation in the case of the hip joint

89

Table 4 4 Correlation (r) and level of significance (p) for the relationship between jump height and selected segmental parameters during eccentric phase_____________________________________ _______________ __________________ _______________ __________________

Ankle peak velocity Knee peak velocity Hip peak velocity Ankle work done Knee work done Hip work doner______ P_________ r______ p r______ p_________ r p_________ r p_________ r______

Gb G m 0 64 0 004

123

‘ 456

_

0 58 0 036

0 68 0 004" " 0 59 “ 0 0f6

0 68 0 004

0 64 ” 0 67

0 68 0 53

0 005 0004 0 004 0 034

-- - y " 8 9

0 62 0 013 061 0 004-0 56 _ 0 023

101112

~ -062 0 015

131415

0 59 0016 0 59 0016 -0 54 0 029 0 57 0 021_

1718 0 52 0 045 0 77 <0 001 0 83 <0 001 -0 51 <0 001 0 84 <0 001 0 82 <0 001

90

Kinematics and kinetics at start of concentric phase

Table 4 5 below details the mean amplitude of the BCOM, the vertical ground

reaction force (vGRF) at the start of the concentric phase, and the joint angles and instantaneous joint moments at joint reversal (JR) for each joint The point where the BCOM reversed its vertical direction was taken to be the start of the concentric phase

of the whole body The point where the rotation of the joint changed direction, called

joint reversal (JR), was taken to represent the start of the concentric phase for an individual joint Measures of inter-subject and mean values of intra-subject

variability are presented Inter-subject variability was approximately three times the

intra-subject variability The angle of the hip at JR was more variable at both inter-

subject and intra-subject levels compared to the ankle and knee joints, suggesting less

of a consistency in temporal strategies employed at the hip

Table 4 5 Mean and variance values of whole body and segmental kinematics and kinetics for the group and average variance for individuals at the start of the concentric phase_________________________________________________

Group IndividualMean SD CV Mean SD Mean CV

Amplitude (m) 0 33 0 07 20 2 0 02 66vGRF (N kg ') ___ __ 10 72 271 25 3 0 84 85Ankle angle (rad) 0 96 " 0 09 90 0 03" 2 6Knee angle (rad) 1 38 0 25 18 1 0 05 42Hip angle (rad) 1 11 0 30 27 3 0 09 96Coupling time ankle (s) 0 12 0 04 33 8 0 03 27 6Coupling time knee (s) 0 09 0 03 29 7 0 02 186Coupling time hip (s) 0 07 0 02 24 9 0 01 100Ankle moment (N m kg ') 2 57 0 83 32 4 0 34 14 1Knee moment (N m kg ') Hip moment (Nmkg )

2 78 1 02 36 6 0 32 1233 44 1 00 29 1 0 35 11 2

91

Table 4 6 details the correlation coefficient (r) and level of significance (p) for the

relationship between jump height, and amplitude of movement of the BCOM, joint

angles at JR, the vGRF at the start of the concentric phase and the joint moments at

JR A negative correlation between jump height and joint angle at JR suggests a

greater joint flexion was observed in jumps of greater height While no direct

measure of joint range of motion (ROM) was taken, starting position was

standardised, therefore a lesser joint angle at JR can be assumed to be a greater ROM

None of the kinematic parameters outlined were significantly correlated with jump

height at the group level However, at the individual level five subjects had a

significant correlation between jump height and amplitude of movement, while two,

six and five had significant correlations between jump height and the ankle, knee and

hip angles at JR, respectively The majority of correlations between jump height and

the amplitude of movement were positive, suggesting greater amplitude occurred on

average in jumps of greater height, while there were predominately negative

correlations between jump height and the joint angle at JR, suggesting greater joint

flexion was evident in jumps of greater height The exception to this were subjects

nine and 14, for subject nine the opposite relationship was observed for both amplitude of movement of the BCOM and knee angle, additionally for subject 14

knee angle was positively correlated with jump height, suggesting jumps greater

height also had on average less knee flexion

The vGRF at the start of the concentric phase was found to be correlated with jump

height at a group level when the mean of each subjects 15 jumps were used in the

analysis (G m) At a segmental level, only the ankle joint instantaneous moment at JR was marginally correlated with jump height at a group level (G m and G b) The number of significant correlations at an individual level was three and four for the moment at ankle and hip joints at JR respectively, while no significant correlation

between jump height and the moment at the knee joint at JR was found for any

individual At the group level coupling time was only found to be correlated with

jump height at the hip joint (G m r = -0 48, p = 0 43) At an individual level, the

coupling time of the ankle joint was found to be correlated with jump height for a

single individual (subject 1 r = -0 56, p = 0 025) and at the hip joint for two (subject

14 r = -0 53, p = 0 035, subject 18 r = -0 73, p = 0 002)

92

Table 4 6 Correlation (r) and level of significance (p) for the relationship between jump height and kinematic variables at the start of the concentricphase ____________ ____________________________________________ ________________ ___________________________________

Amplitude Ankle ROM Knee ROM Hip ROM vGRF at start Ankle moment Knee moment Hip momentof phase at JR at JR at JR

r P r P r P r P r P r P r P r PGb G m 0 47 0 048

0 47 0 49

0 050 0 038

1234 "56

0 66 0 69 0 76

0 004 0 003 0 001 0 53 0 034

0 64 0 64

0 007 “ 0 008

0 69 0 67 0 80

0 002 0 0Ö5

<0 001

-

0 68

-0 60

0 004

0015

--------------- ------------------

7~ " 8 910""1112

-0 56 0 023 --------- -------- -0 57 0 021 ------ — -----0 53 0 041

- -0 62 001

131415 0 52 0 047

-0 57 0 64

0 021 0014

0 63 0 0090 64 0011 0 57 0 027 0 64

0 710015 0 005

161718 0 84 <0 001 0 80 <0 001 0 84 <0 001 0 91 <0 001Note JR joint reversal

vGRF Vertical ground reaction force

93

Kinematics and kinetics during the concentric phase

Table 4 7 below outlines the mean rise in the BCOM from standing to take-off

(BCOMs to), the duration of the concentric phase, the peak vGRF, the peak whole

body power and the total positive work done during the concentric phase Measures

of inter-subject and mean values of intra-subject variability are presented As can be seen from table 4 7 greater variability between subjects for whole body kinetics

during the concentric phase exists compared to intra-subject variability

Table 4 7 Group mean, SD and CV and individual SD and CV for whole body kinematics and kinetics for during the concentric phase _________

MeanGroup

SD CVIndividual

SD Mean CVBCOMs-to (m) 0 11 0 02 13 0 001 88Phase duration (s) 0 29 0 06 19 8 0 02 66Peak vGRF (N kg') 11 88 2 07 174 0 57 5 0Peak Power (W kg') Work Done (J kgY)

48 94 6 92 14 1 1 71 3 56 02 0 83 139 0 33 60

Note BCOMs-to Difference in height of BCOM between standing and take-offPeak vGRF Peak vertical ground reaction force

Table 4 8 shows the correlation coefficient and corresponding level of statistical

significance for the relationship between jump height and the BCOMs t0, the duration

of the concentric phase, the peak vGRF, the peak whole body power and the total

positive work done during the concentric phase The BCOMs t0, the duration of the

concentric phase, the peak vGRF and the peak whole body power were not correlated with jump height at a group level but were significantly correlated with jump height

for six, five and three individuals, respectively In contrast, the peak whole body

power and the total work done were positively correlated with jump height at both the group level (G m and G b) and for nine and eleven individuals, respectively The positive correlation between jump height and phase duration for four of the five individuals suggests jumps of greater height also had on average a longer concentric

phase For one individual (subject 9) a negative correlation between jump height and

the duration of the concentric phase was evident, suggesting jumps of greater height

had shorter concentric phases on average for this individual

94

Table 4 8 Correlation (r) and level of significance (p) between jump height and whole body kinematics and kinetics during the concentric phase______________________

BCOMs-to Phase duration Peak vGRF Peak Power Work Doner P r P r P r P r P

Gb 0 50 0 035G m 0 56 0014 0 48 0 043

1 0 73 0 0012 0 66 0 0053 0 83 <0 0014 0 66 0 009 0 83 <0 0015 0 71 0 002 -0 66 0 006 0 77 0 0016 0 62 0 01 0 72 0 002 0 80 <0 0017Q

0 63 0 009 0 67 0 005O9 -0 56 0 024_ 0 77 <0 00110 0 80 <0 OOf 0 61 0 01611 0 69 0 00512 0 74 0 002 0 52 0 04413 0 71 0 003 0 62 001314 0 79 <0 001 081 <0 001 0 86 <0 00115 0 65 0 009 0 83 <0 001 0 75 oo°i16 0 72 Ö oof17 0 54 0 03718 0 67 0 005 0 67 0 004 -0 68 0 004 0 86 <0 001

Table 4 9 below outlines the mean values for the peak joint moments and powers and

the amount of work done at each joint during the concentric phase Measures of mter-

subject variability and mean values of intra-subject variability are presented Inter-

subject variability was over two-fold that of intra-subject variability In addition,

comparison to the equivalent whole body measures outlined in table 4 7 reveal there

was also a greater than two-fold increase in variability of segmental measures

Table 4 9 Mean and variance of segmental kinematics and kinetic for group and average variance for individuals during the concentric phase_______________

MeanGroup

SD CVIndividual

Mean SD Mean CVPeak ankle moment (N m kg ') 3 10 0 56 18 1 0 23 75Peak knee moment (N m kg ’) Peak hip moment (Nmkg )

3 15 0 85 26 9 0 34 1123 74 0 89 23 7 0 29 84

Peak ankle power (W kg ') 22 11 4 98 22 5 2 04 " 9 2Peak knee power (W kg !) Peak hip power (W kg )

14 42 4 10 28 4 1 63 11 513 71 3 80 27 7 1 42 11 0

Ankle work done (J kg]) 2 01 0 42 " 21 1 0 19 9 2Knee work done (J kg ]) Hip work done (J kg )

1 68 0 57 34 2 0 19 11 72 33 0 81 34 8 0 29 13 8

95

Table 4 10 details the correlation coefficient and corresponding level of statistical

significance for the relationship between jump height and peak moment, peak power

and positive work done at all three joints Both peak ankle moment and peak ankle power were found to be correlated with jump height at the group level (G m and G b)

and at an individual subject level for six and five individuals, respectively Five of

the six individuals exhibited a positive correlation between jump height and peak

ankle moment, as inline with the group analysis, while subject 18 had a negative

correlation Peak knee moment was not found to be significantly correlated with jump height at a group level, but two subjects had individual negative correlations

These two individuals also exhibited a positive relationship between knee angle at JR

and jump height outlined in table 4 6 Peak knee power was significantly correlated

with jump height at the group level but only when the best jumps were used in the

analysis (G b) and also for two individuals, but contrasting relationships were

observed (subject 4 r = -0 50, subject 15 r = 0 66) Neither peak hip moment nor

power were significantly correlated at a group level with jump height but was

significantly correlated at an individual level for five and six individuals, respectively

The amount of positive work done at the ankle joint was positively correlated with jump

height at a group level (G m and G b) and for eight individuals, suggesting jumps of

greater height also had more work was done on average Both knee and hip work done

were not significantly correlated at a group level (G m and G b), however, hip work

done was found to be positively correlated with jump height for six individuals While a

significant correlation between knee work done and jump height was evident for four

individuals, contrasting relationships were observed For two individuals jumps of

greater height had more work done at the knee on average, while the opposite was true for a further two subjects The two individuals whose knee work done was negatively correlated with jump height, also had a positive correlation between jump height and knee joint angle at JR, and between jump height and negative knee work done (tables 4 6 and 4 4 respectively), suggesting a lesser knee joint ROM and less knee work was

done in jumps of greater height

96

Table 4 10 Correlation (r) and level of significance (p) between jump height and segmental kinematics and kinetics during the concentric phasePeak ankle Peak knee Peak hip Peak ankle Peak knee Peak hip Ankle work Knee work Hip workmoment moment moment power power power done done doner p______ r p______ r p______ r p______ r p _r p______ r p_______r p_______r p

G b G m

0 48 051

0 042 0 030

0 53 0 58

0 025 0012

0 52 0 028 061 0 58

0 007 0012

1 0 59 0 020 0 58 00182 0 55 0 026 0 58 0 0203 0 55 0 021 0 70 0 0024

_ - -0 048 081 <0 001

5 0 65 0 0076 0 64 0 008 0 57 0 022 0 59 0016 0 55 0 027

"7 " 0 ^6 "~0 025 0 58 00188 0 6 0 00189 -0 59 0015 0 64 0 008 0 54 0 029 -0 69 0 0031011 0 56 0 03112 0 70 0 003 0 70 0 00413 0 69 0 007 0 70 0 00414 0 65 0 006 0 57 0 021 0 73 0 001 0 73 0 001 0 86 <0 001 -0 56 0 026 071 0 00215 0 59 0 021 0 57 0 026 0 66 0 007 0 68 0 005 0 69 0 00516 05 8 00151718 -0 65 0 006 -0 66 0 005 0 93 <0 001 0 85 <0 001 0 67 0 004 0 85 <0 001

97

The total amount of work done is the summation of the amount of work done at the

individual joints Alteration in the relative contribution of each joint to total work done may affect jump height, table 4 11 outlines for all subjects the average

percentage contribution of each joint Differences in the relative contribution of each

joint to total work done are evident between subjects For example, for subject two

the relative contribution of the ankle joint to total work done was 49 5% but was only

22 8% for subject nine, the hip joint contribution ranged from 56 5% for subject 16 to

14 0% for subject five No correlation was observed at the group level (G m and G b) between jump height and the relative contributions of each joint to total work done

At an individual level correlations are outlined in table 4 11, when no value is present

a non-significant correlation was observed

Table 4 11 Percentage of total work done by each joint and correlation with jump height_______________________________________________

% work % work % work % ankle % knee % hipankle knee hip r r r

G m 33 8 27 9 38 3Gb 34 8 26 7 38 5

1 32 9 27 0 40 12 49 5 21 2 29 33 28 8 25 4 45 8 -0 53 0 484 27 4 20 8 51 8 -0 56 0 715 41 9 44 1 140 0 546 52 8 32 4 14 87 34 0 31 2 34 88 31 9 22 0 46 1 -0 60 0 609 22 8 38 8 38 4 0 57 -0 69 0 6310 41 5 26 5 32 011 29 5 24 3 46 212 26 1 38 5 35 4 0 5613 28 0 28 0 44 014 33 9 37 3 28 815 36 5 195 44 0 0 73 -0 77 0 55

~ 16 28 7 14 8 56 5 “17 29 4 14 8 55 8 0 4518 33 2 35 6 31 2 -0 78 -0 84 0 86

98

4 11 Jump predictors based on group analysis

Investigation into which biomechanical parameters determine jump performance has

predominantly been focused on a group level The biomechanical parameters

correlated at a group level may differ to those found at an individual level Table 4 12

details the slope and level of significance of the linear relationship for variables that

exhibited a significant correlation with jump height at a group level (G m and G b)

and the number of subjects that exhibited a correlation with jump height for these

parameters at an individual level

Table 4 12 Descriptions of relationship between jump height and mechanical parameters that where correlated at a group level and number of individuals that also exhibited a correlation with jump height for these parameters_____

Gb G mNumber of individuals with sig correlation (p<0 05)

Peak whole body power Slope 0 003 0 005 9concentric phase (W) p-value 0 010 <0 001Peak negative velocity Slope -0 070 -0 087 4ofBCOM(ms') p-value 0 026 0 008Peak power eccentric Slope 0 000 0phase (W) p-value 0015Whole body positive Slope 0 027 0 026 11work done (J) p-value 0 035 0 043vGRF at start on con Slope 0 008 2

phase (N) p-value 0 048Duration Eccentric Slope -0 114 4phase (s) p-value 0 050Peak negative hip Slope -0 030 4angular velocity (rad s ) p-value 0 004Positive ankle work Slope 0 058 0 062 8done (J) p-value 0 007 0012Peak Ankle Power (W) Slope 0 004 0 005 5

p-value 0 025 0012Peak Ankle moment Slope 0 030 0 042 6(Nm) p-value 0 042 0 030Ankle moment @ JR Slope 0 025 0 027 3(rad) p-value 0 050 0 038Peak knee power (W) Slope 0 006 0

p-value 0 028Hip coupling time (s) Slope -1 309 2

p-value 0 043

99

4 12 Selection of jump parameter to alter to enhance jump height

When making a decision of which biomechanical parameter to train, four questions

must be taken into consideration Firstly, how strong is the relationship between the

biomechanical factor and jump height7 Secondly, how much will a change in the biomechanical factor increase jump height7 Thirdly, by how much can the

biomechanical factor be trained7 Fourthly, what is the magnitude of biomechanical

factor for the individual relative to the group mean7 The strength of the relationship

between a biomechanical factor and jump height is revealed by the correlation

coefficient The amount, by which an increase in one unit of a parameter corresponds

to an increase in jump height, is determined by the slope of the relationship While

the standard deviation and the CV don’t directly answer how much the factor can be

varied they provide a measure into how much the factor varied

The four parameters outlined in table 4 13 provide good examples of differing

relationships regarding variability and the relationship between changes in the

parameter and jump height Where no slope for an individual is present, that

parameter was not found to be significantly correlated with jump height for that

individual In order to compare slopes across parameters of differing units the

‘Adjusted slope’ was taken as the slope divided by the mean of the parameter As can

be observed from the CV and the mean absolute value of the slope, hip negative work

done exhibits a relatively large variability and a steep slope on average In contrast,

peak ankle moment has a relatively small variance and a gentler gradient for the relationship of the change with jump height Peak knee angle at JR and peak hip

power provide examples of low variability/steep slope and high variability/shallow

slope, respectively However, these patterns did not hold for all individuals For the knee angle at JR, which in general had a steep slope and low variability, different relationships were demonstrated at an individual level Subject 15 had a low variance

and steep slope, while subject four had a large variance and a gentler slope

100

Table 4 13 Mean, variance and slope for selected parameters to highlight issue regarding selection parameters to altering to achieve increases in jump height

SubjectHip negative work done (J)

Mean SD CV slopeKnee angle at JR (radian)

Mean SD CV slopePeak ankle moment (Nm)

Mean SD CV slope MeanPeak hip power (W)

SD CV slope1 0 54 0 15 27 8 I 14 0 03 26 3 39 0 35 103 0 050 14 14 1 48 10 52 0 36 0 12 33 3 1 65 0 04 24 4 49 0 12 2 7 0 021 13 44 1 02 763 0 66 0 18 27 3 -0 048 1 44 0 04 2 8 3 21 0 17 5 3 21 64 1 77 824 0 70 0 32 45 7 -0 024 1 60 0 09 56 -0 081 2 62"”” 0 22 84 18 79 1 26 675 0 24 0 07 29 2 -0 133 1 50 0 05 3 3 -0 161 2 80 0 22 79 7 11 0 79 11 16 0 22 0 08 36 4 -0 121 1 46 0 04 2 7 4 01 021 5 2 8 36 0 79 94 00137 ‘"0 55 0 12 21 8 1 49 0 04 27 3 13 0 23 73 13 03 1 65 12 78 0 62 0 16 25 8 1 54 0 11 7 1 3 37 0 16 4 7 15 72 1 04 66 0 0039 0 43 0 17 39 5 0 90 0 04 44 0 053 2 21 0 47 21 3 0 056 11 55 1 24 107 0 00510” 0 38 0 33 86 8 ”l 35" 0 07 " 52”” 3 65 0 20 5 5 13 47 1 33 99 “11 0 65 0 24 36 9 1 45 0 06 4 1 2 84 031 109 16 83 1 80 10 712 0 49 0 14 28 6 0 88 0 04 45 3 39 0 48 142 11 12 1 68 15 113 ~ 0 52 0 13 25 0 ”” "130 ‘ 0 05" 3 8 2 65 0 14 5 3 14 02 1 17 8 314 0 34 031 912 -0 087 0 98 0 05 5 1 0 223 2 67 0 15 5 6 0 094 10 52 2 63 25 0 001315 0 61 0 09 14 8 1 67 0 02 1 2 -0 464 321 0 17 53 0 050 14 19 0 93 6616 0 73 0 18 24 7 1 57 0 05 32 2 82 0 18 64 18 35 1 16 63 ÒÒÓ417 0 64 0 26 40 6 1 56 0 05 32 2 74 0 18 66 15 51 2 33 15 018 0 42 0 37 88 1 -0 063 1 40 0 09 64 -0 250 2 64 0 25 95 -0 073 8 94 1 91 21 4 0 130

Mean 40 2 0 080 3 9 0 205 79 0 057 11 2 0 028Adjusted slope 0 157 0 149 0018 0 002

Note Mean of slope, calculated from absolute values of slope Adjusted slope = slope / mean

101

4 13 Variability and parameter identification

Table 4 14 details the mean jump height, standard deviation and range of jump

heights observed for each individual Also included is the average coefficient of

variability (CV) of all the kinematic and kinetic parameters examined, the number of

significant relationships with jump height observed for each individual and of those

the number them that are also evident in the group model, irrespective of the sign of the relationship, are presented

Table 4 14 Mean, standard deviation and range of jump height observed for each individuals and the number of significant relationships observed________ ____

Jump Height (m) VariablesNumber of Number also in

Subject Mean SD Range Mean CV significant group model1 051 001 0 03 75 4 32 0 50 001 0 05 93 7 53 0 49 001 0 05 83 7 14 0 49 0 01 0 05 11 7 11 25 0 46 0 01 0 04 92 13 26 0 43 0 02 0 07 84 8 47 0 42 " 0 02 ” 006 113 "5 48 0 42 001 0 03 80 5 49 0 42 0 01 0 04 11 9 10 210 0 42 0 02 0 05 9 1 3 111 041 0 02 0 08 145 2 212 041 0 02 0 06 109 4 413 0 40 0 02 0 06 120 6 314 0 40 0 02 0 08 103 18 715 0 39 001 0 06 89 10 516 0 38 0 01 0 03 114 2 117 0 36 0 01 0 04 104 1 018 0 34 0 03 0 11 159 21 5

Mean 0 43 0 02 0 06 105 76 30

The range in jump heights observed was found to be significantly correlated with the number of significant variables found for an individual (r = 0 59, p = 0 009)

However, no significant correlations were found when the standard deviation of jump

height was examined This suggests that individuals who displayed a greater range of

jump heights during the experiment also exhibited a greater number significant

correlations between jump height

102

4 2 Coordination and jump performance

Table 4 15 details the mean timing delay between key events of adjacent joint pairings The time delays are defined as the time occurrence of an event at the

proximal joint less the time occurrence of the same event at the distal joint The key

events selected were the timing of joint reversal (JR.), the peak instantaneous joint

moment, the peak instantaneous joint power and the peak joint angular velocity

during the concentric phase (MV) A negative value indicates that the event occurred

in the proximal joint prior to the distal joint Measures of inter-subject and mean

values of intra-subject variability are presented The timing of peak angular velocity

was least variable, while the timing of peak joint moment was most variable

Table 4 15 Mean timing of joint pairings for key events and measures of inter-subject and intra-subject variability ______________________________________

Group IndividualVariable Mean SD c v Mean SD Mean CV

knee-ankle JR (s) 001 0 10 9 0 0 04 1 0hip-knee JR (s) -0 03 0 04 -1 2 0 02 -0 2knee-ankle Peak moment (s) -0 03 0 12 -3 9 0 09 -8 5hip-knee Peak moment (s) -0 07 0 13 -1 8 0 08 0 7knee-ankle Peak power (s) -0 03 0 02 -0 7 001 -0 3hip-knee Peak power (s) -0 07 0 04 -0 6 0 03 -1 2knee-ankle MV (s) -0 02 0 01 -0 4 001 -0 4hip-knee MV (s) -0 03 0 01 -0 4 001 -0 3Note JR Joint reversal

MV Peak angular velocity of the jointknee-ankle time delay from event occurring at the knee to event occurring at the ankle hip-knee time delay from event occurring at the hip to event occurring at the knee

A proximal-to-distal sequence was observed on average for all individuals for both the sequencing of peak angular velocity and peak joint power However, the order of sequencing was not so distinctive and consistent for the initiation of joint extension (JR) The group on average extended the hip before the ankle, and the ankle joint began to extend before the knee However, at an individual level variation in this pattern was present Nine individuals exhibited a proximal-to-distal sequence on

average in all three joints, two exhibited a distal-to-proximal in all three joints, while

seven did not have a proximal-to-distal or a distal-to-proximal sequential pattern but a

combination (5 individuals H-A-K, 1 individual K-H-A and 1 individual A-H-K)

103

No significant correlation with jump height was observed for any of the temporal joint

pairing at a group level (G m and G b) At an individual level a number of

correlations between temporal joint pairings and jump height were observed but were

predominately limited to only one or two individuals One individual (subject 10)

exhibited a significant correlation between jump height and the time delay between JR

of the knee and the ankle joint (r = 0 53) and the timing between the hip and the knee

joint (r = - 0 83) with delays of 0 003s and -0 026s, respectively suggesting jumps of

greater height also had longer delays (a minus value in delay indicates the proximal

joint extended before the distal joint) Another individual (subject 11) exhibited a

positive correlation between jump height and the time delay between JR of the hip

joint and JR of the knee joint (r =0 54), which occurred with an average delay of

0 127s

Correlations between jump height and the delay between peak moments of adjacent

joints were only significant for one individual (subject 14), the delay between the

knee and the ankle peak moments (r = 0 84) and between the hip and the knee joints (r

= -0 71) occurred with average delays of -0 253s and 0 223s, suggesting jumps of

greater height had shorter delays

The delay between the peak power of the hip joint and the knee joint was negatively

correlated with jump height (subject 18 r = -0 712) for one individual and positive

for another (subject 16 r = 0 490), with average delays of -0 115s and -0 089s, respectively suggest a longer delay for subject 18 and shorter for subject 16 Finally,

the delay between peak angular velocity of the knee and the ankle joint was

negatively correlated with jump height (subject 9 r = -0 546) for one individual occurring with an average delay of -0 013s While the delay between peak angular velocity of the hip joint and that of the knee joint was negatively correlated for three

individuals with average delays of -0 039s, -0 029s and -0 059s All correlations suggested jumps of greater height also had longer delays

104

4 3 Rate of force development and CMJ performance

Table 4 16 below details the mean RFD over the intervals A, B, C, Dl, D2, E, F, G,

HI and H2 (Figure 3 4), and the rate of power development over the first 60ms of the

concentric phase, for the ankle, knee and hip joints, and the whole body Measures of inter-subject variability and mean values of intra-subject variability are presented

Table 4 16 Mean and variance values of RFD of ankle, knee and hip joint moments, and whole body vGRF ___________________________________________

MeanGroup

SD CVIndividual

Mean SD Mean CVAnkle JR to TO (E) -2 49 1 14 -45 8 0 55 -22 3Knee JR to TO (E) -2 43 1 22 -50 1 0 39 -15 9Hip JR to TO (E) -2 60 1 00 -38 4 0 32 -124Whole body JR toTO(A) -15 36 6 48 -42 2 1 68 -109Ankle min to JR (F) 0 68 " 0 08 115 “ 0 13 19 1Knee min to JR (F) 0 59 0 10 174 0 13 22 0Hip mm to JR (F) 0 95 0 09 95 0 16 168Whole body min to JR (B) 4 36 0 56 129 0 91 20 9Ankle min to peak (G) " 0 69 0 11 16 3 " Ö 13~ 19 0Knee min to peak (G) 0 57 0 10 182 0 15 25 8Hip min to peak (G) 0 99 0 10 102 0 18 177Whole body min to peak (C ) 4 36 0 53 122 0 94 21 6Ankle min to 50% (HI) 1 17 0 15 13 1 021 179Knee min to 50% (D2) 1 14 0 20 180 0 23 20 3Hip min to 50% (D2) 1 88 0 28 15 0 0 30 160Whole body min to 50% (Dl) 9 36 1 32 14 1 1 94 20 7Ankle 50% to peak (H2) ~ ‘ 0 85 0 20 23 5 0 25 29 4Knee 50% to peak (H2) 0 66 0 21 31 9 0 33 49 4Hip 50% to peak (H2) 1 07 0 17 164 041 37 9Whole body 50% to peak (D2) 4 17 0 55 13 2 1 49 35 6Ankle power in first 60ms "9 51 “ 6 59 69 2 14 85 156 2Knee power in first 60ms 19 88 3 96 199 8 26 41 6Hip power in first 60ms 43 86 4 58 104 5 87 13 4

Table 4 17 indicates the significant correlations observed between jump height and

the rate of force development (RFD) The RFD over the interval from JR to take-off

was negatively correlated with jump height for ankle and hip joint moments, and for

the whole body vGRF (ankle r = -0 53, hip r = -0 53, whole body r = -0 50) The

RFD for the knee joint was correlated with jump height only when the best jump was

put forward for analysis (r = -0 47) The negative correlations indicate that jumps of

105

greater height a more rapid decline in force (Figure 3 4, A and E) A positive

correlation over the intervals B, C, D, F, G and H, suggests that a greater RFD was

observed in jumps of greater height The RFD from the instance of minimum vGRF to JR was correlated with jump height for the ankle and hip joint moment and the

whole body vGRF (ankle r = 0 52, hip r = 0 57, whole body r = 0 55) Similarly,

correlations were observed between jump height and RFD from the instance of

minimum vGRF to peak force for the ankle and hip joint moment and the whole body

vGRF (ankle r = 0 51, hip r = 0 55, whole body r = 0 52) The interval between the

minimum and maximum force was sub-divided into two phases, from minimum

vGRF to 50% peak moment (or vGRF) and from 50% peak moment (or vGRF) to

peak moment (or vGRF) Correlations with jump height were observed for all joints

and whole body for only the first phase (ankle r = 0 52, knee r = 0 53, hip r = 0 66,

whole body r = 0 63), while no significant correlations were observed over the

second phase The only correlation at a group level between the rate of power

development (RPD) and jump height was observed for the hip joint (r = 0 48)A number of individual correlations were observed but were at best only present in six

individuals in the case of minimum vGRF to peak moment for the hip, and in

development of knee power over the first 60ms of the concentric phase For a number

of parameters both positive and negative correlations were observed, suggesting that

for some individuals a greater RFD was desired while for others it was detrimental

106

Table 4 17 Correlation (r) between jump height and (1) rate of force development and (11) power development over selected intervals

JR to TO min to JRMoment or vGRF

min to peak mm to 50% 50% to peakPower

JR to JR+60msA K H W A K H W > X $ A K H W A K H W A K H

G b -0 55 -0 47 0 47 -0 53 0 52

G m -0 53 -0 52 -0 50 0 52 0 57 0 55 0 51 0 55 0 52 0 52 0 53 0 66 0 63 0 48

1 0 59

2 0 59

_3_ 0_80__ 0 82 061 0 78 0 63 0 77 0 74 0 72 0 77 0 62

4 0 69

5 -0 49

__ 6__ -0 49

7 0 668 0 53 0 57 0 62 0 57 0 64 0 59 061 0 55 0 58 0 64

9 061 -0 56 -0 65

10

11 0 56 -0 57

12 0 56 -0 57

13 -0 60 -0 53 0 57 0 73 0 66 0 62 0 58 0 74 0 59 0 6014 0 56 0 5615 -0 53 0 79 -0 67 0 67 051 0 63 0 49 0 64 0 59 0 58 0 52 0 52 0 65

16

17 -0 81 -0 81

18 0 56 -0 71 0 55 -0 56 0 73 0 57 -0 58 0 86Note A = ankle, K - knee, H = hip, W = whole body

JR = joint reversal TO = take-offmin = instant where vGRF was at minim

107

4 4 Comparisons of kinetics between the CMJ and the DJ

The magnitude of selected kinematics and joint kinetics were compared between the

CMJ and drop jumps from 30cm (DJ30) and 50cm (DJ50), to determine the suitability

of DJs as a means of training to enhance CMJ performance Table 4 18 details the

mean changes in the magnitude of jump height, amplitude of the BCOM, duration of

the eccentric and concentric phases, peak negative and positive whole body power in

the DJ (DJ30 and DJ50) compared to the CMJ Table 4 19 details the mean changes

in magnitude of joint moment at JR, peak joint moment and peak joint power for the

ankle, knee and hip joint in the DJ (DJ30 and DJ50) compared to the CMJ All values

are given as the magnitude observed in the DJ less that observed in the CMJ (negative

values indicates DJ less the CMJ) Finally, table 4 20 summaries the results from

table 4 19 also indicating the parameters which were found to be significantly

correlated with jump height in the CMJ as outlined in section 4 1

As can be seen from table 4 18, jump height during DJ30 did not differ significantly

from the CMJ at the group level but DJ50 was on average 2cm lower than the CMJ

At an individual level, nine subjects achieved a reduced jump height for the DJ30 and

the DJ50, while three and two individuals achieved greater jump height during the

DJ30 and DJ50, respectively The DJ30 was executed with reduced amplitude of

movement of the BCOM at the group level, and for 11 of the 18 individuals There

was no significant difference in amplitude of movement between DJ50 and CMJ at

the group level, but reduced amplitude was evident for 10 of the 18 individuals In

contrast, greater amplitude of movement was observed for three and four individuals

for DJ30 and DJ50, respectively In comparison to the CMJ reduced duration on

average was observed for both the eccentric and concentric phases for both drop

heights at the group level of analysis No significant difference was observed

between DJ30 and DJ50 for the duration of the eccentric phase but the duration of the

concentric phase was on average longer in the DJ50 than the DJ30 (G m) At an

individual level, no subject used an extended eccentric phase during a DJ, however,

three individuals had an extended concentric phase for DJ50 The vGRF at the start

of the concentric phase in the DJ did not differ to CMJ at a group level for both DJ30

and DJ50 (G m and G b) At an individual level, eight subjects had greater vGRF at

the start of the concentric phase, while six experienced greater in the DJ50

108

Table 4 18 Differences in jump height achieved and whole body kinematics and kinetics between CMJ and DJ from 0 3m and 0 5mump height (m) Amplitude (m) Duration Eccentric Duration concentric vGRF at start o f Peak whole body Peak whole body

phase (s) phase (s) concentric phase (N) negative power (W) positive power (W)30 50 30 50 30 50 30 50 30 50 30 50 30 50

G b -0 01 -0 01 -0 06* -0 04 -031* -0 32* -0 06 * -0 05* 0 32 -0 09 -39 89* -72 24*o -3 26 -3 67G m -0 01 -0 02* -0 05*o -0 04*o -0 31* -031* -0 06* -0 04*o 0 23 -0 05 -37 10* -75 50*o -3 70* -5 00*o

1 -0 01* OOlo -0 16* -0 09*o -0 28* -0 27* -0 12* -0 08*o -0 19 001 -28 18* -50 25*o 0 60 -1 76*o2 -0 06* -0 08*o -0 07* -0 07* -0 17 -0 17* -0 06* -0 06* 1 63* 1 67* -45 71* -98 12*o -4 98* -6 25*3 -0 04* -0 04* -0 12* -0 13* -0 27* -0 27* -0 10* -0 11* 2 25* 2 20* -39 17* -88 95*o -1 01 0 004 -0 02* -0 04*0 -0 15* -0 15*” -0 22“* “ -0 22* -0 13* -0 13* 5 06* 5 10* -47 48*“ -102 50* o” 1 94* " " 6 6 1 * “5 -0 05* -0 03* -0 00 0 00 -0 13* -0 13* 001 0 02* -3 10* -2 51* -24 93* -50 52*o -11 95* -10 93*6 0 00 -0 06*o 0 03* 0 07*o -0 24* -0 21* 001 0 05*o -2 15* -3 20*o -40 69* -88 88*o -7 98* -13 65*o7 -0 01 -0 04*o -0 04* -OOlo -0 38* -0 36 -0 06* -OOlo 2 86* 0 63o -55 65* -10241*o -6 92* -9 40*o8 001* 0 03*o -0 01 0 07*o -0 24* -0 23*o -0 08* -0 04o -3 30* -3 11* -12 56* -26 75*o -11 12* -1274*o9 -0 02* -0 04* -0 05 -0 06 -0 73* -0 73* -0 08* -0 06*o 2 48* 2 63* -27 82* -57 02*o -7 70* -6 86*10'~ “ ”-0 03*“ "-0 04* ” " -0 16* -5 15* " -0" 34* ” -0 32* -0 11* " -0 11* 2 96* 3 17*“" -51 37* " -56 94*“ ' 8 71* 7 37* "11 0 01 -0 02o 0 00 -0 04*0 -0 33* -0 37* -0 04* -0 06* -0 62 -0 32 -55 62* -117 20*o -3 62* -4 82*12 -0 01 -0 01 -0 04* -0 00o -0 18* -0 15*o -0 02* OOOo -3 15* -3 24* -22 30* -43 56*o -4 49* -5 43*13 0 02* OOlo -0 06* -0 04*o -0 32* -0 26* -0 06* -0 02*o -0 09 -1 19*o -35 71* -102 67*o -1 36* -3 48*o14 001 -0 00 -0 07* -0 04*o -0 54* -0 52* -0 10* -0 08* 091* 0 72 -26 55* -72 76*o -2 46 -5 07*o15 0 06* 0 03*o 0 06* 0 07* -0 27* -0 24* -0 00 0 02*o 1 96* 0 54 -35 08* -65 80*o -1 20* -6 6216 -0 01 0 00 ~ 0 02* ‘ " 0 02* -0 47“* “ " -0 46* 0 00~ 0 01 -0 21 -0 58 -42 38*” -78 76*o -5" 33 -4 96*17 -0 03* -0 02* -0 09* -0 09* -0 33* -0 34 -0 11* -0 12* 1 05 1 38* -34 02* -80 28*o -3 84* -3 81*18 -0 02* -0 01 -0 09* -0 06*o -0 26* -0 31* -0 09* -0 05*o -0 42 -0 92* -36 81* -89 66*o -2 34* -2 89*

Note * = differs from CMJ at a = 0 05 level o f significance o = differs from DJ30 at a = 0 05 level o f significance -ve = CMJ > DJ

109

Peak whole body negative power was greater in the DJ30 than the CMJ and greater

again in the DJ50 This pattern was also present at an individual level for all subjects

except one (subject 10) that did not exhibit a difference between the DJ30 and the

DJ50 (G m and G b) At a group level peak whole body positive power was less in

the DJ30 than the CMJ and less again in the DJ50 (G m only) At an individual level

lower peak whole body positive power was observed for 12 and 14 subjects for DJ30

and DJ50, respectively, while five of these exhibited a reduced power in the DJ50

than the DJ30

The use of DJ as a training intervention is primarily to provide an overload to specific

elements of the neuromuscular system For DJ to be an appropriate means of

overloading desired elements of the neuromuscular system, magnitudes of segmental

kinetic parameters need to be greater in the DJ than those experienced during the

CMJ Table 4 19 details the difference in joint moment at JR, peak joint moment and

peak joint power for the ankle, knee and hip between the DJ and the CMJ (DJ - CMJ)

A visual summary is provided in table 4 20

At the group level, ankle moment at JR was not found to be significantly different in

the DJ compared to the CMJ However, at an individual level ankle moment was

greater for seven and eight of the 18 individuals for the DJ30 and the DJ50,

respectively, while it was found to be lower in a further four and five for the DJ30 and

the DJ50, respectively More similarity in the results between the group and

individuals analysis was observed at the knee and hip joints At the group level, knee

moment at JR was greater in the DJ than the CMJ and was found to be less for the hip

joint These patterns were replicated for the majority of subjects at an individual level

(knee DJ30 = 15, DJ50 = 12, hip DJ30 = 13, DJ50 =15) No significant difference

was observed for peak ankle moment between the DJ and the CMJ at the group level

However, at an individual level greater peak ankle moments were observed for both

DJ30 and DJ50 than during CMJ in four individuals Peak knee moments were found

to be greater during the DJ at the group level of analysis and the pattern was

replicated at the individual level in 12 of the 18 individuals Peak hip moment was

found to be less in the DJ than the CMJ at both the group level, and for 17 of the 18

individuals for both the DJ30 and the DJ50

110

Table 4 19 Differences in joint kinetics between CMJ and DJ from 0 3m and 0 5mAnkle moment at JR

(Nm)30 50

Knee moment at JR (Nm)

30 50

Hip moment at JR (Nm)

30 50

Peak ankle moment (Nm)

30 50

Peak knee moment (Nm)

30 50

Peak hip moment (Nm)

30 50

Peak ankle power (W)

30 50

Peak knee power (W)

30 50

Peak hip power (W)

30 50

G b 0 05 0 05 0 96* 0 67*o -1 19* 1 06* -0 18 -0 12 0 79* 0 65 -1 51* -1 14* 461* -5 28* 11 08* 10 63* -6 95* -6 00*

G m 0 22 0 12 1 03* 0 83*o -1 17* -1 03* -0 08 0 13 0 87* 0 86* -1 38* -1 17* 3 34* -4 26*o 9 44* 9 47* -6 24* -5 72*

1 0 57* 0 43* 0 76* 0 53* -1 32* -0 52*o 0 72* 0 49* 1 08* 0 88* -1 19* -0 35*o 1 70 -1 04o 7 89* 7 68* -5 71* 401*

2 0 42* 0 44* 2 22* 2 20* -2 16* -1 95* 0 16 0 20 1 93* 2 03* -3 46* -3 45* -4 06* -3 92* 13 86* 15 77* -8 82* 9 48*

3 0 86* 1 07* 1 64* 2 35* -1 09* 1 28* 0 63* 0 82* 1 76* 2 13* -1 04* -1 21* -1 54 -1 11 9 67* 13 27* 6 00* -8 18*

4 2 95* 2 97* 3 28* 3 26* -2 62* -241* 201* 2 05* 2 89* 2 73* -3 62* 361* 5 56* 5 70* 16 16* 18 07* -14 25* 1491*

5 -0 92* -0 96* 001 -0 06 -1 63* 1 42* -0 94* 0 99* 0 12 0 13 -1 53* -1 31* -1102* ■11 53* 9 05* 11 31*o -5 26*o -4 50*

6 -0 33 -0 97*o 0 35* 0 09o -061* 0 68* -0 52* -0 90*o 0 15 -0 02 -0 79* -0 90* 8 66* - 11 53*o 8 00* 4 99*o -2 28* -3 21*

~T Ó 48* OOlo l“07* ~0 49*o 0 33 0 30” -0 04“ -0 32*o” ” 0 3 4 “ 5 09 " -0 29”' “ -0 38* 5 65* "-6Ì8* 7 24* T84*o~ 0Tr ” -~2 57*~

8 -0 57* -0 70* 0 20 0 06 2 86* 2 36*o -0 76* 0 95* -0 85 -0 98 -2 64* -2 14*o -9 05 -11 21 -0 53 -0 81 -11 04* -9 76*

9 0 34 0 08 1 40* 1 71* 0 15 0 24 0 05 -0 12 0 63* 0 96* -0 52* -0 49* 251* -3 02* 4 30* 3 66* -3 04* -2 76*

10 1 36* 1 63* 2 50* "202“ “ 2 57*0” -1 97* 0 98* "T 41* r6 7 * " ”l ì 4*“ -3 46* -2 00*o 5 08* “4 27*- y 4 32~ - 18 59* 10 69* ”” -8 17*o

11 -0 02 -0 12 1 11* 0 95* -0 39 -0 56* 0 20 -0 19 0 36* 0 57* -0 66* -0 65* -2 59 -3 01 9 37* 7 62* -7 32* -741*

12 -0 80* -1 05* 0 08 -0 31 -1 42* -1 07* -0 56* -0 65* 0 12 0 26 -1 40* -1 07* -3 88* -4 38* 9 79* 8 19* -5 05* -2 65*o

~ r r 0 18 -0 20 0 98* 0 46*o -1 47* -1 44* -0 06 -0 31*o 0 92* 0 45*o -1 40* -1 35* -1 30 -3 86*o 11 77* 11 92* -6 16* -5 70*

14 0 32 0 49* 0 55* 0 29 -0 30 0 lOo -0 41* -0 42* 0 47* 0 24* -0 79* -0 33*o -3 07* -3 99* 9 74* 6 44*o -4 16* -2 20*o

15 0 73* 0 94* 2 14* 1 47*o -0 67* -0 80* -051* -0 30* 1 90* 1 40*o -0 70* 0 65* -6 89* -6 74* 10 68* 7 88*o -5 49* -4 13*o

16 “ -0 33* -0 57* 0 58*“ 0 38* " -0 13 ~0 40* ~ -“0 31*“ ~ -0 50*o~ ~ 004 0 08 “ ~ -048* ~0 69* ” " “ 4 56* ~-5~3~9*~~■“ 3 88* ““ 5 70*o -5 59* -5 02*

17 021 0 36* 1 28* 1 26* -091* -0 37o -0 21 -0 06 1 18* 1 37* -061* -0 13o -6 17* -6 07* 11 97* 10 49* -7 24* -5 95*

18 0 16 -0 07 0 58* 0 19o -1 47* 0 94*o 0 12 -O il 0 82* 0 57*o -1 51* 1 07*o -1 20 -3 42*o 1001* 9 26* -4 98* -3 98*

Note * = differs from CMJ at a = 0 05 level o f significanceo = differs from DJ30 at a = 0 05 level o f significance

111

At a group level of analysis both peak ankle joint power and peak hip joint power

were found to be lower in both the DJ30 and the DJ50 compared to the CMJ This

was evident at the individual level for all subjects for hip power and, 11 and 12 of the

18 subjects, respectively, for the DJ30 and the DJ50 However, for two individuals

(subject 4 and 10) peak ankle joint power was greater in the DJ than the CMJ

Increases in the magnitude of peak knee joint power were also observed in the DJ

compared to the CMJ at both the group level and at an individual level for 17 of the

18 subjects Differences between peak knee joint power in the DJ30 and the DJ50

were evident in six individuals but not at a group level However, four exhibited a

greater peak knee power in the DJ50, while another two exhibited greater magnitude

in the DJ30 Differences between the DJ30 and the DJ50 were also observed for the

peak ankle power at both the group level (G m only) and at the individual level for

four subjects, all with greater magnitude in the DJ30 No difference was observed in

peak hip joint power at a group level but five subjects exhibited greater magnitude in

the DJ30 at the individual level

While a number of kinetic variables have been seen to be overloaded in the DJ (DJ30

and DJ50) in comparison to the CMJ, both at a group and individual level, in order for

DJs to produce a positive enhancement in the CMJ performance, the variables

overloaded must be limiting factors of CMJ performance For detail of the

identification of performance limiting factors, we refer the reader to the section 4 1

Table 4 20 details the significant differences between the CMJ and the DJ, indicates

the kinetic parameters were been found to be correlated with jump performance

Of the two of individuals that exhibited positive correlations between ankle moment

at JR and jump height, only one was overloaded in the DJ and in the case of hip

moment at JR none of the four While four individuals that were positively

correlation between peak ankle moment and jump height, only one showed

overloaded in the DJ compared to the CMJ None of individuals positively correlated

between jump height and peak hip moment, peak ankle power or peak hip power,

exhibited an overload of these parameters in the DJ compared to the CMJ However,

subject 14 who was positively correlated between jump height and peak knee joint

power had a greater magnitude of peak knee joint power in the DJ50 compared to the

CMJ, and greater again in the DJ30

112

Table 4 20 Kinetic parameters overloaded in the DJ compared to the CMJ, with parameters significantly correlated with jump height m CMJ indicated

vGRFstart Ankle Knee Hip Peak ankle Peak knee Peak hip Peak Peak Peak ankle Peak knee Peakconcentric moment at moment at moment at moment moment moment negative positive power power povphase (N) JR (Nm) JR (Nm) JR (Nm) (Nm) (Nm) (Nm) power (W) power (W) (W) (W) (W

Gb • <50<30 '0 ns • <30 10 ^0 <30 <50 >0 '*) < 30, 50 M)G m • ns • <50<30 0̂ Sh ns • < 30, 50 50 <30 <50 • " 10 Si # < 30, 50 30

1 <30, 50 <30, 50 SO *0 <30, 50 • <30, 50 so <30 <50 n ̂ <30, 50 ''O2 <30, 50 <30,50 • <30, 50 tn Oh • <30, 50 io ' <30 <50 10 <30,50 :o3 <30, 50 <30, 50 < 30, 50 *0 so <30, 50 <30, 50 >0 sn • <30 <50 ns hs <30, 50 304 <30, 50 <30, 50 <30, 50 X*) n* <30, 50 <30, 50 '0 <30 <50 <30, 50 <30, 50 <30,50 o o5 10 H) j() s( o ns '0 10 <0 n** "0 S; <30 <50 ' * *0 10 J <30, 50 1(;6 10 50 ;o so <30 JO SO _ ru 10 “O <30 <50 >0 SO • 30 * ) • <50<30 30_ _

<50<30 <30 <50 <30 n so n • <30 <50 >0 so • H) *0 <50<30 3*8 SO • H) ns *0 io So us s{) .0 <30 <50 Mi -{) A) s ) IN >09 <30, 50 r <30, 50 m • n <30<50 o 10 so <30 <50 ns • M) S'* • <30, 50 10

16” <30, 50“ <30,50 < 30, 50 <30750 <30, 50 S() >* <30 <50 <30,50 • <30, 50 <30, 50 so11 ns rK <30, 50 fO <30, 50 so <30 <50 m sn • n> <30, 50 »3012 <30, 50 *0 SO ns H) -0 XQ -o ns »30 v* <30 <50 *0 ~0 • 10 so • <30, 50 5 L13" :0 V ns • <50<30 30 "■‘0 • m) <50 <30 i7)~ >) • <30 <50 10 so <30, 50 1 d14 <30 <50 <30 lb 10 SO • <30, 50 50 >0 <30 <50 ">0 • 30 • <50<30 • V)15 <30 <30, 50 <50<30 M) -o <50 <30 30 '»l • <30 <50 "0__ • 10 M> • <50<30 , so.

” 16“ rw <50, 30 1 *>u • is i{) ~ <30 <50 " • <30<5017 <50 <50 <30, 50 ns <30, 50 3>i <30 <50 'U "0 *0 M) <30, 50 3018 i s <30 50 io • ns o <50 <30 o M) ^0 • <30 <50 * ̂ **0 SO <30, 50 yv

Note < = magnitude o f parameter greater in the DJ than the CMJ• = positive correlation between parameter and CMJ jump height at a = 0 05 level o f significance o = negative correlation between parameter and CMJ jump height at a = 0 05 level o f significance

113

Discussion

114

The predominate methodology that has been utilised in biomechanical analysis, is to

compare differences between individuals, referred to as group analysis This group

approach assumes that the movement strategy for all individuals is the same However, not every athlete has the same neuromuscular capacity (e g individual joint

power, rate of power production and joint dominance), anthropometries (e g limb

length and relative mass) and muscle morphology (e g percentage muscle fibre type),

and diverse movement strategies have been observed It may be more appropriate to

make inferences about an individual’s movement strategy by treating each individual

as their own experiment group, examining differences between repetitions of an

individual’s own performance, referred to as individual analysis The results of the

two approaches will be discussed, firstly, in relation to what biomechanical factors

correlate with countermovement jump (CMJ) performance and secondly, the

difference in the kinetics between the CMJ and the drop jump (DJ)

The section will start with a discussion of the differences between the magnitude of inter-subject and intra-subject variability The factors found to be correlated with

jump height at a group level will be compared with the factors found at an individual

level Possible reasons will be outlined for the discrepancies between the two forms

of analysis Questions that need to be addressed over the selection of which

biomechanical parameter to be trained with a view to enhancing CMJ performance

will be outlined Finally, the results comparing the neuromuscular overload in the DJ, over that of the CMJ, will be discussed in relation to the potential use of the DJ as a

training intervention to enhance CMJ performance

5 1 Inter-subject verses Intra-subject variance

As expected, variability was evident both between the 18 subjects (inter-subject variability) and within the 15 jumps of each individual (intra-subject variability)

Across all parameters there was greater inter-subject variability than intra-subject

variability In many cases inter-subject variability was two to three times that of

intra-subject, which was similar to the differences found by Aragon-Vargus and Gross

(1997a, 1997b) for vertical jump kinematics and kinetics The inter-subject

variability reflects not only the varying strategies employed, but also differences due

115

to neuromuscular capacity, anthropometries and muscle morphology, while mtra-

subject variability reflects changes only in the jump strategy used

Whole body kinematics and kinetics were generally less variable than the

corresponding joint measures, both at the inter-subject and intra-subject level This

can be partly attributed to the compensating ability of the multilinked human system,

allowing whole body kinetics to be maintained in the face of changes at one joint

being offset by changes at another (Dowling and Vamos, 1993) Kinetic measures

were found to be in general more variable than kinematic measures These findings

have also been observed in other studies of vertical jumping (Aragon-Vargas and

Gross, 1997a, Rodacki et al, 2001, van Soest et al, 1985) and other movements such

as walking and running (DeVita and Skelly, 1990, Dufek et al, 1995) Again this is

likely to be a reflection of maintaining an overall kinematic movement strategy,

which can be produced through a variety of joint kinetic strategies

There was greater variability in parameters in the eccentric phase than the concentric

phase Since one of the requirements for maximizing jump height is to maximise

mechanical energy at take-off (Bobbert and van Ingen Schenau, 1988), this results in

a relatively consistent configuration of the body at take-off, with all the joints of the

lower extremities being nearly fully extended (Bobbert and Van Soest, 2001) The

use of a greater variability in the eccentric phase and at the transition between the

phases may be due to variations having a smaller effect on jump performance, or that

the performer has less capacity to integrate information from the eccentric phase than

the concentric phase to optimise jump performance

5 2 Group analysis

A statistical analysis at the group level, where differences between individuals have been examined, has predominantly been employed in identifying factors that relate to

performance success In the biomechanical literature the selection of a representative

value for an individual has predominately taken two forms the mean magnitude of values observed and the value corresponding to the best performance Table 4 12

outlines the mechanical parameters that were correlated with jump height at the group

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level, using the best performance (G b) and the mean values (G m) In general the

biomechanical factors revealed when using the best performance were also revealed

when using the mean values However, the converse was not true, just over half the

biomechanical factors revealed using the mean values were also revealed using the

values from the best jump When the values from the best performance were used,

the magnitude of all biomechanical parameters from that jump are regressed against

the jump height achieved, not just those parameters that were responsible for

achieving that height As a number of diverse biomechanical strategies may be

selected to maximise jump height, the use of the values from the best jump may

obscure the identification of factors relating to jump height at the group level The

presence of individual strategies still persists when mean values are used, but as it is

the “typical” characteristics that are put forward for analysis, it may prove a more

robust method

In the present study, the group approach identified a number of parameters that were

significantly correlated with jump height (table 4 15), peak negative vertical velocity

of the BCOM (r= 0 60), peak positive power (r= 0 56), peak negative power (r= 0 58),

positive work done during the concentric phase (r= 0 48), vGRF at the start of the

concentric phase (r= 0 47) and the duration of the eccentric phase (r= -0 47)

Taking the eccentric phase first, the related factors of a high peak vertical velocity and

power, and a short duration, may be beneficial to improving jump height Only two

studies appear to have directly examined the relationship between mechanical

parameters of the eccentric phase and jump performance Dowling and Vamos (1993)

found both peak vertical velocity (r= 0 29) and power (r = 0 30) to be correlated with

jump height but the strength of the relationships were less than those reported in the present study While Aragon-Vargas and Gross (1997a) did not explicitly examine the negative velocity of the BCOM, they did find peak negative impulse to correlate

with jump height (p<0 02) These findings are also consistent with the observation that improvements in jump height in the CMJ over that of the squat jump (SJ) are

greater with faster and shorter eccentric phases (Bosco et al, 1981, Cavagna, 1977,

Komi, 2000)

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Vertical ground reaction force (vGRF) at the start of the concentric phase was found

to be correlated with jump height (r= 0 47) This is inconsistent with the findings of

Dowling and Vamos (1993) who found no significant correlation Bobbert et al

(1996) examined improvements in jump height in the CMJ over the SJ using

mathematical modelling based on actual jump data They attributed the enhancement

to greater force at the start of the concentric phase in the CMJ, allowing larger joint

moments during the first part of joint extension At the whole body level both peak

positive power and positive work done were found to correlate with jump height

Other researchers have also reported peak power to correlate with jump height

(Aragon-Vargas and Gross, 1997a, Dowling and Vamos, 1993, Harman et al, 1990)

In these studies correlations (r) of 0 68, 0 93 and 0 86, respectively, were reported,

compared to 0 76 within the present study One possible reason for the lower

correlation found by Aragon-Vargas and Gross (1997a) is they did not normalise for

body weight When power was not normalised for body weight within the present

study, the correlation fell to 0 56 The strong association between jump height and

peak power indicates that high forces need to be accompanied by rapid execution

This would suggest that training should aim to develop strength specifically at high

velocities (Dowling and Vamos, 1993) In contrast to the present study, previous

studies have found peak vGRF to correlate significantly with jump height (Dowling

and Vamos, 1993, Harman et al, 1990) The amount of positive work done in the

concentric phase was positively correlated with jump height m the present study No

previous studies appear to have examined how a change in the amount of work done

was relates to jump performance While Aragon-Vargas and Gross (1997a) did not explicitly examine work done, they found average power and phase duration were

positively related to jump height in many prediction models As work done is the

product of average power and duration, a relationship between jump height and work done may have existed

No relationship was found between the duration of the concentric phase and jump height, supporting previous findings by Dowling and Vamos (1993) However,

Aragon-Vargas and Gross (1997a) included concentric phase duration as part of a

prediction model for take-off velocity, suggesting it was negatively related to jump

height at a group level

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While knowledge of the relationships between jump height and jump mechanics at the whole body level is important, more specific information can be achieved by

examining the relationship at the joint level At the joint level a number of parameters

correlated significantly with jump height peak angular velocity of the hip during the

eccentric phase (r= 0 64), ankle positive work done (r= 0 58), peak ankle power

(r=0 58), peak knee power (r= 0 52), peak ankle moment (r= 0 51), ankle moment at

joint reversal (r= 0 49) and coupling time at the hip (r= -0 48)

In the present study the joint that exhibited the greatest number of significant

correlations with jump height was the ankle joint In contrast, Aragon-Vargas and

Gross (1997a) found hip kinetic parameters (peak hip power and peak hip moment)

exhibited the strongest correlations, with peak knee power only included within

models already containing hip kinetic parameters None of their models included

ankle kinetic measures However, at an individual level many of their models contain

peak ankle power and peak ankle moment, but hip kinetic parameters still dominated their models (Aragon-Vargas and Gross, 1997b) Variation between individuals in

the relative contribution of each joint to total work done has been found (see table

4 11) (Hubley and Wells, 1983) It is possible that the joints showing significant

correlations with jump height may be specific to each sample group of individuals

5 3 Comparison between group and individual level

If comparable results are observed for both the group analysis and the individual

analysis, this would suggest that all individuals perform alike and the group approach

may be suitable for identifying performance strategies for all individuals However, it was found that no parameter that was significantly correlated with jump height at the group level was also significantly correlated for all subjects at an individual level

The two variables with the greatest degree of correspondence between the two forms of analysis were total positive work done and peak positive power, correlating at an individual level in 11 and 9 of the 18 individuals, respectively Aragon-Vargas and

Gross (1997b) similarly found peak whole body power to be a significant predictor of

jump height for all eight individuals they examined While they did not examine

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work done per se, average power and duration of the concentric phase were also

significant for all individuals

For the eccentric and the transition phases, few subjects exhibited significant

correlations at an individual level for the whole body parameters that were found to

correlate significantly at the group level Only four subjects exhibited a correlation at

an individual level for peak velocity and eccentric phase duration, while no

individuals had correlations for peak negative power Additionally, in contrast to the

concentric phase, where consistencies in the direction of the relationships were observed, directly opposing relationships were observed in the eccentric phase Three

individuals exhibited a negative correlation between jump height and the duration of

the eccentric phase, matching the results of the group analysis, while a single subject

(subject 4) exhibited a positive relationship A negative relationship suggests a fast

and forceful downwards movement of the body in the eccentric phase would benefit

jump performance, enabling a high velocity of stretch of the muscles and greater force

at the start of the concentric phase, which have been previously reported to enhance

jump height (Bosco et al, 1979, Bosco et al, 1982a, Komi, 2000) The positive

relationship observed for subject four is in contradiction to this However, the

relationship can be explained by an interaction of some of the parameters In

additional to the correlation with phase duration, the amplitude of movement of the

BCOM was also correlated with jump height (r= 0 69) for this subject To accommodate the greater range of motion over which to develop force, extended

eccentric and concentric phases were therefore employed This suggests the presence

of two different strategies, one involving a rapid and shallow movement which

utilises the SSC, and the other which involves greater movement amplitude, providing

a greater distance over which to apply force

The results of the group and individual analysis appear to be less comparable at the

joint level than at the whole body level (table 4 12), with at best eight individuals exhibiting a correlation for a parameter that was also revealed at the group level (i e

ankle work done) Additionally, there were a greater number of parameters exhibiting

opposite relationships with jump height between individuals (e g ankle moment at

JR) Differences were more evident in the eccentric and transition phases than the concentric phase Aragon-Vargas and Gross (1997a and 1997b) also found a reduced

9

120

comparability between the two forms of analysis at the joint level However, the

biomechanical parameter they found to exhibit the strongest correlation with jump

height at the group level was still evident m six of the eight subjects at the individual

level, and was also the single best predictor of jump height for one individual (subject

W) (Aragon-Vargas and Gross, 1997a) The reduced comparability between the

results of the group and individual analyses at the joint level is possibly a reflection of

the compensatory ability of the multi-segmental nature of the human body, allowing

the same whole body kinetic pattern to be achieved using numerous combinations of

joint kinetic strategies (Hubley and Wells, 1983)

In the present study, several parameters were also found to be significantly correlated

with jump height for a number of subjects at an individual level, but were not significantly correlated at a group level The amplitude of movement of the BCOM,

the vertical difference of the BCOM from standing to take-off, the duration of the

concentric phase (table 4 8), peak hip moment, peak hip power and work done at the

hip (table 4 10), were all found to be correlated with jump height in at least five

individuals, but not at the group level Aragon-Vargas and Gross (1997a and 1997b)

found this same pattern for the amplitude of movement of the BCOM, the vertical

difference of the BCOM from standing to take-off and the duration of the concentric

phase However, while Aragon-Vargas and Gross (1997b) also found peak hip power

and peak hip moment to be related to jump height at an individual level, correlations were also observed at the group level (Aragon-Vargas and Gross, 1997a)

At the group level, the hip joint was found on average to contribute the most to total work done, but this was not observed in all subjects The relative contribution that

each joint made to the total work done was not found to be correlated with jump height, for any joints at a group level However, a number of significant correlations were observed at the individual level (table 4 11), suggesting while no ideal pattern

may exist for all individuals, an optimum pattern particular to an individual may still exist In addition, both positive and negative correlations were observed between

jump height and work done at various joints

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5 4 Coordination

At a group level the hip extends on average 0 03 seconds before the knee, with the

ankle extending 0 01 seconds before the knee However, when the average sequence

for an individual was calculated, this hip-ankle-knee sequence was only exhibited by

five subjects Nine individuals had a proximal to distal sequence and two subjects

had a distal to proximal sequence Two subjects had some other combination of joint extension This mixed pattern of joint reversal (JR) has been previously observed

(Aragon-Vargus & Gross, 1997a, Jensen et al, 1991, Rodacki et al, 2001, Rodacki et

al, 2002) Rodacki et al (2001) found that three of the twelve subjects in their study

extended the ankle before the knee, and 21 of the 52 subjects in the study by Aragon- Vargus & Gross (1997a) extended the joints in a hip-ankle-knee pattern A shorter

delay between the JR of the hip and the knee was observed in the present study (knee

0 03s after the hip), compared to other studies (Jensen et al, 1994, Rodacki et al,

2001, Rodacki et al, 2002)

Peakjoint moments followed a proximal to distal sequence, with the peak hip moment

occurring on average 0 07 seconds before the knee, followed by the peak ankle moment on average 0 03 seconds later A proximal to distal sequence was only

observed in ten individuals However, a proximal to distal sequence of peakjoint

power was found in all individuals, which is consistent with the findings of Rodacki

et al (2001) and Rodacki et al (2002) The delay is also comparable to the 0 023

seconds and 0 046 seconds found by Rodacki et al (2001) and Rodacki et al (2002),

respectively However, while Rodacki et al (2002) found a delay between peak knee

power and peak hip power of 0 088 seconds, which is comparable to the average

delay of 0 07 seconds in this study, Rodacki et al (2001) found a slightly greater delay of 0 187 seconds

A proximal to distal sequence of peakjoint angular velocity was also found at the group level and in all individuals, in the present study, which is consistent with the

findings of Jensen et al (1994) However, a proximal to distal sequence was not

observed by Rodacki et al (2001), where peak hip angular velocity occurred 0 01

seconds before the ankle and knee, nor was it observed by Rodacki et al (2002),

where hip and ankle peak velocities occurred simultaneously, followed by the knee

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0 012 seconds later While small delays were evident in these studies (see table 2 19),

marginally greater delays occurred in the present study

None of the time delays were correlated with jump height at a group level Two

possible explanations for this are, firstly, that the sequencing is already optimised as

the skill is well learnt Secondly, that while an optimal timing may exist for an

individual, these optimal sequences differ between individuals, perhaps due to

differences in neuromuscular capacity and anthropometries

While no significant relationship was observed at a group level between jump height

and the delay in JR between adjacent joints, significant correlations were observed for

two individuals One individual had a positive correlation between jump height and

the delay between knee JR and ankle JR (r=0 529), and a negative correlation with the

delay between the hip JR and the knee JR (r= -0 832) Another individual had a

positive correlation between jump height and the delay between hip JR and knee JR

(r=0 537) It is unknown how much the delay should be altered as correlations only

report the sign/direction of a change, but not the magnitude of change It is possible

the relationship may change once a critical delay is achieved This is one of the

limitations of the correlation method

5 5 Inter-subject analysis verses Intra-subject analysis

The predominant approach to identifying performance driving or performance

limiting biomechanical factors is to undertake a group based analysis By comparing

individuals, it is assumed that a significant relationship reflects a more optimum movement strategy Similarly, if no relationship is present for a given variable, it is assumed that the magnitude of the variable does not affect performance This group based approach presumes that a single, ‘abstract’ optimal movement strategy exists

and it can be applied to all individuals This would be true if everyone was physically identical However, individuals differ in their neuromuscular capacity (e g individual

joint power, rate of power production and joint dominance) their anthropometries (e g

limb length and relative mass) and their muscle morphology (e g percentage muscle

fibre type) Therefore, no single optimal movement strategy may be present In

123

consequence, the negative effect of a group based analysis may be that it identifies an

‘optimal’ movement strategy that is in fact detrimental to the performance of an

individual In addition, a movement strategy that would benefit many individuals

may not be observed in a group analysis, simply due to a contrasting strategy from a

few individuals masking its occurrence Given that the present study clearly found

differences in results using a group based in comparison to an individual based

correlation analysis, it is important to at least examine the theoretic implications of a

causal relationship being revealed when the biomechanical parameters are

systematically altered and the relationship with jump height follows the same pattern

as observed in the correlation analysis

The identification of a casual relationship may not always provide a definitive answer

as to whether the parameter should or should not be trained to enhance jump

performance When a mechanical parameter is related to jump height at the group

level (Figure 5 la), it is suggested that all individuals should train this parameter However, this may not always be the case, a situation may arise where a strategy

present in a majority of individuals (e g 80%) dominates the group analysis,

suggesting all individuals (Figure 5 lb) should train this biomechanical factor

However, the training of this biomechanical factor may not be beneficial to the

minority (e g 20%) of the other individuals in the group, or may in fact be detrimental

to their performance Similarly, when no relationship is present at a group level it

does not necessarily imply that this parameter is not related to jump performance for

some individuals Firstly, a case where contrasting strategies between individuals

mask each others detection with correlation analysis may exist (Figure 5 lc) For

example, some individuals may increase power at the hip joint while others find it

more fruitful to increase the power of the ankle joint, resulting in jumps of greater height with both low and high peak ankle power, potentially obscuring the strategies at the group level Secondly, if little variability in the mechanical parameter is present at the group level, an underlying relationship may not be revealed by correlation analysis (Figure 5 Id) This low variance may be due to an optimum existing and be widely employed, resulting in the mean for each individual being centred on a

common point A selection of a more heterogeneous sample group may increase the

variability and the underlying relationship may be revealed

124

A , B c D

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J ? è ) - ®

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Mechanical Parameter

Figure 5 1 Possible relationships between jump height and a mechanical parameter

If a relationship between the magnitude of a biomechanical parameter and jump

height is observed at an individual level, this suggests that the strategy of altering this

factor could increase jump height, indicating the benefits to training this factor

Conversely, if no relationship is found for an individual, it may suggest that this factor

should not be trained However, an underlying relationship with jump height may

still exist, and may not have been revealed in the correlation analysis purely due to

insufficient intra-subject variability The low intra-subject variability may be caused

by the current and limited level in neuromuscular capacity imposing a constraint or

the individual may have settled into a none optimum, invariant movement pattern

simply because they have never attempted other movement strategies

While it is possible that the same kinematic and kinetic strategy would be revealed

using both a group and an intra-subject analysis, results from the present study

indicate little commonality (table 4 12) For example, peak eccentric power

correlated significantly at a group level, but no individuals exhibited a significant correlation When comparing the results of a group and an individual analysis a number of outcomes are possible, table 5 1 represents the six possible scenarios

Table 5 1 Representation of possible scenarios between group and individual analysisGROUP CORRELATION

YES NOINDIVIDUALCORRELATION

ALL 1 2SOME 3 4NONE 5 6

125

At one end of the spectrum, scenario 1 refers to when a parameter is significantly

correlated with jump height at both the group level and for all subjects at an

individual level, explaining both why some individuals jump higher and why some

jumps of an individual are higher than other jumps At the other end of the spectrum

of possible responses, scenario 6 refers to where no correlation with jump height at

either the group or the individual level is present Neither of these scenarios occurred

for any of the variables in the present study Scenario 5 is where a correlation is

present at a group level, but not at an individual level for any subjects, this is the case

within the present study for peak eccentric whole body power Since differences were

observed between individuals, this may reflect differences in neuromuscular

capacities Scenario 2 is the case where the parameter is correlated for all subjects at an individual level, but not at a group level This suggests all subjects should tram this factor Two possible explanations may be put forward to why no correlation was

observed at the group level Firstly, the magnitude of the mechanical factor may

indeed be important in jump height achievement, but the individuals’ means were

centred on a common point, possibly an optimum level, thus reducing group

variability Secondly, the level of the mechanical factor is important, but individuals

have different optimums The differing optimums may be related to the differences in

physical characteristics of the individuals, or due to differing strategies being

employed by individuals For example, one individual may use a large range of

movement and small eccentric loading, while another may use a small range of

movement and large eccentric loading, but both individuals may produce the same

jump height

In the present study the majority of parameters fall under scenario 3 and 4, where not

every individual performed the same Scenario 3 presents a situation where a parameter is correlated with jump height at both the group level and at the individual level for a number of subjects This was the case for ankle positive work done in the

present study Scenario 4 is where some individuals exhibit a correlation, but no correlation was observed at the group level, as was the case in the present study for

peak hip power

126

The results of the group analysis may suggest that the better performers utilised a

certain strategy but it may not be true to say that, if all individuals utilised that strategy they would increase performance, as the strategy may not be suitable for

them given their physical characteristics While differing strategies may be the result

of individual perceptions of performance outcome, it is the physical characteristics of

an individual that may play the greatest role in the selection and success of a given

strategy It is possible that these physical characteristics may predispose individuals

to certain strategies and therefore different optimums Due to differences in limb

length corresponding position of the BCOM at the start of the concentric phase

between individuals may require different knee angles (Alexander, 1995), in turn the

optimum knee angle may depend on the current neuromuscular capacity

(Thorstenssen et al, 1976) and muscle morphology (Bosco et al, 1982a) of the

individual

Bosco et al (1982a) found that for individuals with a high percentage of fast twitch

muscles, jumps of smaller knee amplitude resulted in a greater enhancement of kinetics than larger amplitudes in the concentric phase of a CMJ over that of a SJ

However, for individuals with greater number of slow twitch fibres jumps of larger

amplitude allowed more time for force to build up and resulted in a greater percentage

relative enhancement of kinetics than jumps of small amplitude Therefore for a

group of individuals with diverse muscle morphology and stature, potentially jumps

of differing amplitude of movement will result in jumps of greater height for these

individuals, as highlighted by the differing relationships observed for amplitude of

movement of the BCOM (table 4 6) and duration of the eccentric phase (table 4 2)

127

5 6 Questions arising over the selection of which parameters to alter

Four questions should be considered when deciding whether a biomechanical parameter is worth training to enhance jump height Firstly, how strong is the

relationship between the biomechanical factors related to differences in jump height9

Secondly, how much will a change in the biomechanical factor increase jump height9

Thirdly, by how much can the biomechanical factor be trained9 Fourthly, what is the

magnitude of biomechanical factor for the individual relative to the group mean9 An

indication of the strength of the relationship between the biomechanical parameter and jump height can be revealed by the correlation coefficient (r), the larger

correlation coefficient (r) the more of the variability in jump height can be explained

by the variability in the biomechanical parameter If a strong and significantly

relationship is revealed through correlation, the extent to which a change in the

mechanical parameter causes a change in jump height must be examined Information

regarding the possible extent of the change is available from the slope of the bivariate

relationship The steeper the slope, the more jump height seen to increases when a

change in the biomechanical parameter occurs As can be observed in figure 5 1,

greater jump height is achieved in ‘scenario c’ compared to ‘scenario a’, and in

‘scenario d’ compared to scenario b \ for comparable changes in the biomechanical

parameter However, as can also be observed, a greater increase in jump height is

achieved in ‘d’ than in ‘a’, with a corresponding slope, by virtue of a greater range over which the biomechanical parameter is altered An indication of the potential

range over which the biomechanical parameter can be altered may be revealed by the

sample variance, both intra-subject and inter-subject From the four scenarios outlined in figure 5 1, it is evident that a large slope is not enough to achieve a large

increase in jump height, but the correct combination of slope and variation in the biomechanical parameter is required Finally, the magnitude of the biomechanical factor for the individual, relative to the group, must be considered If an individual

already produces a high magnitude in comparison to the group, there may be less scope for improvement in comparison to an individual demonstrating a lower

magnitude This is evident in a number of training studies, which have shown that the

neuromuscular training response is largest in those who have not previously training

(Plisk, 2001)

128

Figure 5 2 Interaction of variability and slope of relationship between jump height (y axis) and a mechanical jump parameter (x axis)

Examples of the interaction of slope and variance are illustrated in table 4 13 The

mean magnitude, amount of variance (standard deviation [SD] and coefficient of

variability [CV]) and slope, are reported for four jump parameters peak ankle

moment, hip negative work done, peak hip power and knee angle at JR In relation to

figure 5 1, peak ankle moment represents ‘scenario a’, peak hip power ‘scenario b’, knee angle at JR ‘scenario c \ and hip negative work done ‘scenario d’ A comparison

of negative work done at the hip revealed that for subjects 5 and 6, a greater slope of

the relationship with jump height than that for subjects 3,4, 14 and 18 Furthermore, the variance and mean magnitude is lower For these two individuals, it appears that training this parameter may provide a greater increase in jump height than training

another parameter This is true, providing the amount of negative work done can be

increased further In respect to the group mean, this appears possible In the case of subject 16, for peak hip power, both the variance and the slope of the relationship

with jump height are low In this case, it may not be prudent to spend time training

this already high magnitude, and training should centre on a different variable

129

5 7 The use of drop jumps as a means of training the CMJ

The drop jump (DJ) has been used as a training method to enhance countermovement jump (CMJ) performance, with differing levels of success For example, Blatter and

Noble (1979) found that CMJ height increased on average 2 1cm after a training

program involving DJs, while Matavuji et al (2001) observed a 5 6cm increase after a comparable training program However, Brown et al (1986) found no significant

increase after a more extensive training program For DJs to be a successful method

of enhancing CMJ performance they must (1) have a similar movement pattern (in relation to the muscle groups used, the coordination pattern, the joint range of motion

(ROM), the velocity of contraction and the muscle action), (11) provide an overload of

the neuromuscular system, and (in) tram those factors that are related to CMJ height

The DJ clearly provides a close qualitative match with the CMJ in relation to the

movement pattern employed The extent to which the kinetics are overloaded in the

DJ, and the ability of the DJ to overload the specific jump kinetic parameters that relate to differences in performance success in the CMJ are discussed below In

addition, the implications of the differences in findings at a group and individual level

are addressed

Peak whole body negative power was found to be significantly enhanced with

increases in eccentric loading, with the greatest magnitudes produced in the DJ50, followed by the DJ30 and then CMJ These findings were consistent at both the

group level and the individual level, for all but one subject This result is hardly

surprising since when landing in the DJ the BCOM has a higher negative vertical

velocity than that experienced in the CMJ, and increases with drop height

All three knee joint kinetic parameters examined (knee moment at JR, peak knee moment, peak knee power) were greater in the DJ compared to the CMJ, both at the

group level and for the majority of individuals This is consistent with the findings of

Bobbert et al (1986a) at a group level for the bounce drop jump (BDJ) and Bobbert et

al (1987a) for both the counter drop jump (CDJ) and the bounce drop jump (BDJ)

Only one difference was evident at the group level between DJ30 and DJ50, with a

significantly greater knee joint moment at JR produced from DJ30 than DJ50 At an

individual level, drop height had a significant effect on only a small number of

130

subjects knee moment at JR (n = 2), peak knee moment (n = 2) and peak knee power

(n = 6) It appears that while DJs provide a suitable means of overloading the knee

joint kinetics, the effect of drop height may be minimal In contrast to the knee joint,

hip joint kinetics (hip moment at JR, peak hip moment, peak hip power) were lower in

the DJ than the CMJ at a group level, and for the majority of subjects at the individual

analysis level In contrast, Bobbert et al (1986a) found no difference in hip joint

kinetics between the DJ and the CMJ While Bobbert et al (1987a) also found no

difference in peak hip power, they did find lower hip moments at JR for the BDJ and

lower peak hip moments for both the CDJ and the BDJ

At a group level, the vGRF at the start of the concentric phase, ankle moment at joint

reversal and peak ankle moment, were not different in the DJs in comparison to the

CMJ, while peak whole body power and peak ankle power were significantly lower in

the DJ than the CMJ The lack of increase in these parameters is consistent with the

results of Bobbert et al (1986a) for DJs employing comparable movement amplitudes

as the CMJ (CDJ) However, Bobbert et al (1986a, 1987a) observed increased

magnitudes in DJs that utilised a significantly reduce movement amplitude, but

increased peak ankle power was only observed by Bobbert et al (1987a) for DJs with

a greater reduction in movement amplitude (BDJ = 24cm reduction) In the present

study, for these same kinetic measures, a number of individuals exhibited greater

magnitudes in the DJ in comparison to the CMJ Interestingly, these subjects tended

to use a smaller amplitude of movement, which in light of the findings by Bobbert et

al (1986a, 1987a) may explain these findings For example, nine subjects had an increase in ankle joint moment at JR in the DJ compared to the CMJ, with a further

five exhibiting a reduction Of the nine individuals that displayed an increase in ankle

moment at JR, eight utilised a DJ technique with a smaller amplitude of movement, while four of the five with a reduced ankle moment at JR utilised a larger movement amplitude than that of the CMJ Similarly, only four individuals had a greater peak

ankle moment in the DJ than the CMJ and all of these individuals employed 10cm less amplitude of movement in the DJ than the CMJ (the only four individuals in the

study with such a reduction) Finally, two individuals (subject 4 and subject 10) who

had greater peak positive whole body and ankle power in the DJ compared to the

CMJ, utilised a substantial reduction in movement amplitude (16cm)

131

A possible explanation for the effect of a smaller amplitude of movement enhancing

the magnitude of overload in the DJ over the CMJ for selected kinetic variables, may

be that when a small amplitude is used the BCOM must decelerate quicker This may

result in the time that elapses between the peak stretch of the muscles and the start of

the concentric muscle contraction being kept short Bosco et al (1982a) found that a

higher velocity of stretch in the eccentric phase and a higher vGRF at the start of the

concentric phase occurred in jumps with less knee range of motion A short

“coupling time” and a fast stretch have been found to enhance the kinetics on the

concentric phase (Bosco et al, 1981, Cavagna et al, 1968)

The only differences in jump kinetics at a group level between the two drop heights

were a lower whole body peak power, ankle peak power and peak knee moment at JR

in DJ50 than DJ30 A number of differences were observed at the individual level,

the majority suggesting lower kinetics in the DJ50 than the DJ30 It appears that

increasing the amount of negative work done by altering the drop height did not

appear to be a successful method of overloading kinetics

5 8 The suitability of drop jump as a means of training the CMJ

While a number of kinetic variables have been seen to be overloaded in the DJ (DJ30

and DJ50) in comparison to the CMJ, both at a group and individual level, in order for

DJs to produce a positive enhancement in the CMJ performance, the variables overloaded must be limiting factors of CMJ performance Examination of table 4 17

clearly shows that at a group level, of the five kinetic parameters correlated with jump

height, only peak negative power was overloaded This suggests that DJs provide a suitable means of training peak negative power to enhance CMJ height, however, the use of DJ to train the other kinetic parameters does not seem worthwhile At an

individual level, only three subjects experienced an overload in a kinetic parameter

that was correlated with the CMJ height for them It appears that DJs would only provide a suitable means of training the CMJ for these individual However, DJ

training may provide a suitable training stimulus for the CMJ for more individuals

When a biomechanical parameter is correlated with jump height at a group level, it

reflects not only differences in strategies employed but also differences in the

132

neuromuscular capacities between individuals Therefore, a significant correlation at

a group level, may suggest all individuals should train that kinetic factor (e g peak

ankle moment) While overload was not observed at a group level, it was for some individuals and the possibility exist that alteration of the DJ technique of the other

individuals may induce an overload Examination of an individual in isolation may

help in explaining why a lack of response to DJ training However, comparison of an

individuals overload pattern in the DJ to that of other individuals may help to guide

future training interventions using the DJ to provide a training stimulus to enhance

CMJ height

5 9 Conclusion

A number of biomechanical factors were found to be significantly correlated with

CMJ jump height at a group level Those factors that were correlated with jump

height at the group level however, were not always correlated at the individual level,

and visa versa A number of diverse movement strategies were evident at the

individual level, either involving different biomechanical factors or the same factors

but with the opposite relationship with jump height The existence of opposing

strategies may mask the identification of a key strategy at the group level, but also

potentially identify a strategy as being optimal when in fact it may be detrimental to

the performance of some individuals Similar discrepancies between the group and

individual analysis approach were observed for shock attenuation in landing (Dufek et

al, 1995, Lees, 1981) and running (Dufek et al, 1995, Lees and Bouracier, 1994) and

for jump height achievement in the CMJ (Aragon-Vargas and Gross, 1997a, 1997b)

Discrepancies between the results of a group and an individual analysis were also evident in the extent to which kinetic parameters were overloaded in the DJ compared to the CMJ Knee joint kinetics were significantly overloaded in the DJ at both a

group level and for the majority of individuals While no significant overload was apparent for ankle kinetics at a group level, overload was achieved by a number of individuals when a reduced amplitude of movement was used At the hip joint, no

overload in joint kinetics was apparent at either a group or individual level

increasing drop height did not appear to provide an greater overload of joint kinetics

It appears that considerable differences were evident between the group and the

133

individual analyses for both identification of the performance determining factors of

the CMJ and the extent to which the DJ overloaded these factors This may partially

explain the contrasting findings from a number of training studies (Blatter and Noble, 1979, Brown et al, 1986, Matavuji et al, 2001) examining the use of DJs to enhance

CMJ performance

A considerable amount of important information may be lost regarding individual

performance strategies when a group analysis is employed However, the use of

solely individual analyses would not reveal any performance a factor relating to

differing neuromuscular capacities between subjects, and a case for a group analysis

to be used to supplement an individual analysis therefore exists This clearly requires

further research involving training studies to examine which of the two approaches

(group and individual analyses), or what combination of the two, is most appropriate

5 10 Future research

1 ) Once a causal relationship has been established between a biomechanical

parameter and jump height Examine whether individual analysis provides important

biomechanical information that can be used to optimise training interventions (more

so than a group analysis) This can be realised through a number of study designs

a ) Train a large number of individuals and examine if an increase in jump height is greater in those individuals who a relationship exists between jump

height and the trained (overloaded) joint kinetic variable

b ) Train two groups, one group of individuals who all exhibit a relationship

between jump height and the joint kinetic variable being overloaded and one group with no relationship, and examine if there is a difference in the response

to training between the two groups

2 ) Examine a wider range of drop heights and skill levels to determine if that changes

the extent to which an individual's joint kinetics are overloaded

134

3 ) Examine the extent to which exercises to overload the neuromuscular system,

other than the DJ, overload the joint kinetics produced during the CMJ, and to

whether the results differ between a group analysis and an individual subject analysis

If drop height or skill level (research area 2) and exercise (research area 3) change to

varying degrees, the extent to which joint kinetics are overloaded at an individual

subject level, then the results should drive further research into identifying optimal training interventions (research area 1)

4 ) Examine for other sporting actions, other than the vertical CMJ (e g long jump,

high jump), if those correlated with performance success differ at the group and

individual level of analysis

135

References

136

Alexander, R, McN (1995) Leg design and jumping technique for humans, other vertebrates and insects Phil Trans Royal Soc London 347, 235-248

Anderson, F C and Pandy M G (1993) Storage and utilization of elastic strain energy during jumping Journal o f Biomechanics 26(12), 1413-1427

Aragon-Vargas L F and Gross M M (1997) Kinesiological Factors in vertical jump performance differences among individuals Journal o f applied Biomechanics 13, 24-44

Aragon-Vargas L F and Gross M M (1997) Kinesiological factors in vertical jump performance differences within individuals Journal o f applied biomechanics 13, 45-65Asmussen, E and Bonde-Petersen, F (1974) Storage of elastic energy in skeletal muscle in man Acta physiol Scand 91, 385-392

Bangerter, B L (1964) Contnbutive components in the vertical jump The Research quarterly 39(3) 433-437

Bates, B T (1996) Single subject methodology an alternative approach Med Sci Sport Exerc 28(5), 631 -638

Bedi, J F , Cresswell A G Engel, T J , and Nicol, S M (1987) Increase in jumping height associated with maximal effort vertical depth jumps Research Quarterly 58(1), 11-15

Bernstein, N (1967) Coordination and regulation o f movement (1st Ed) Pergamon Publications, NY

Blattner, S and Noble, L (1979) Relative effect of isokinetic and plyometric training on vertical jumping performance Research Quarterly 50, 583-588 Bobbert M F (1990) Drop jumping as a training method for jumping ability Sports medicine 9(1) 7-22

Bobbert, M F , Mackay, M , Schinkelshoek, D , Huijing, P A and van Ingen Schenau (1986a) Biomechanical analysis of drop and countermovement jumps Eur J Appl Physiol Occup Physiol 54(6), 566-573

Bobbert M F Huijing P A and Van Ingen Schenau G (1986b) A Model of the human triceps surae muscle-tendon complex applied to jumping J Biomechanics 19(11), 887-898

Bobbert M F Huijing P A and Van Ingen Schenua G J (1986c) An estimation of power output and work done by the human triceps surae muscle-tendon complex in jumping J Biomechanics 19, 899-906

137

Bobbert, M F , Gerritsen, K G , Litjens, M C and van Soest, A J (1996) Why is counteimovement jump height greater than squat jump height7 Medicine, Science, Sport and Exercise 28(11), 1402-1412

Bobbert M F, van Soest A J (2001) Why do people jump the way they do7 Exerciseand Sport Science Review 29(3), 95-102

Bobbert, M F , Huijing, P A and van Ingen Schenan, G (1987a) Drop jump I Med Sci Sport Exerc 19, 332-338

Bobbert, M F , Huijing, P A and van Ingen Schenan, G (1987a) Drop jump II Med Sci Sport Exerc 19 339-346

Bobbert, M F and van Ingen Scheneau, G J (1988) Coordination on vertical jumping J Biomechanics 21, 249-262

Bobbert, M F & van Soest, A J (1994) Effect on muscle strengthening on verticaljump height A simulation study Med Sci Sport Exerc 26, 1012-1020

Bosco, C and Komi, P V (1979) Mechanical characteristics and fiber composition of human leg extensor muscles Eur J Appl Physiol 41,275-284

Bosco, C , Komi, P V and Ito, A (1981) Prestrech potentiation of human skeletal muscle during ballistic movement Acta Physiol Scand 111,135-140

Bosco, C , Tihanyi, J , Komi, P V , Fekete, G and Apor, P (1982a) Store and recoil of elastic energy in slow and fast types of human sketal muscles Acta Physiol Scand 116, 343-349

Bosco, C Vntasalo, J T Komi, P V and Luthanen, P (1982b) Combined effect of elastic energy and myoelectrical potentiation during stretch-shortening cycle exercise Acta Physiol Scand 114 557-565

Brown M E , Mayhew J L and Boleach L W (1986) Effect of plyometric training on vertical jump performance in high school basketball players J Sport med and phys fitness 26, 1-4

Bozelli, G , Cappozzo, A and Papa, E (1999) Inter- and intra-individual variability of ground reaction forces during sit-to-stand with principal component analysis Med Eng Phys 21(4), 235-40

Burgess-Limerick, R , Neal, R J and Abemethy, B (1992) Against relative timing invariance in movement kinematics Q JE xp Psychol 44(4), 705-22

Button, C , MacLeod, M , Sanders, R and Coleman, S (2003) Examining movement variability in the basketball free-throw action at different skill levels Res Q Exerc Sport 74(3), 257-69

138

Cavaghan PR & Kram, R (1989) Stride length in distance running velocity, body dimensions, and added mass effect Med Sci Sport Exerc 21(4), 467-479

Cavagna, G A , Saibene, F P and Margaria, R (1965) Effect of negative work on the amount of positive work performed by an isolated muscle J Appl Physiol 20(1), 157-158

Cavagna, G A , Dusman, B and Margaria, R (1967) Positive work done by a previously stretched muscle Journal o f applied physiology 24( 1), 21 -32

Cavagna, G A (1977) Storage and utilization of elastic energy in skeletal muscle Ex Sp Sci Rev 5, 89-104

Clark, J E , Phillips, S J and Petersen, R (1989) Developmental Stability in jumping Development Psychology 25(6) 929-935

Clutch, D , Wilton, M , McGown, C and Bryce, G R (1983) The effect of Depth Jumps and weight training on leg strength and vertical jump Res Quart 54, 5-10

Craib M Caruso C Clifton R Burleson C Mitchell V Morgan D (1994) Daily Variation in step length of trained male runners Int J Sports Med 15, 80-83

DeVita, P and Bates, B T (1988) Intraday reliability of ground reaction force data Human movement science 7(1), 73-85

DeVita, P and Skelly, W T (1990) Intrasubject variability of lower extremity joint moments of force during the stance phase of running Human movement science 9(2), 99-115

Diednck, F J and Warren, W H (1995) Why Change Gait9 Dynamics of the Walk- Run Transition Journal o f Experimental Psychology Human Perception and Performance 21(1), 183-202

Dowling, JL & Vamos, L (1993) Identification of Kinetic and temporal factors related to vertical jump performance Journal o f applied Biomechanics 9, 95-100

Dnss T Wandewalle H Monod H (1998) Maximal power and force-velocity relationships during cycling and cranking exercises in volleyball players J Sports med Phy Fitness 38, 286-93

Dufek, J D , Bates, B T , Stergiou, N and James, C R (1995) Interactive effect between group and single-subject response patterns Human movement science 14, 301-323

Dufek, J D and Bates, B T (1990) The evaluation and prediction of impact forces during landings Medicine and Science in Sport and Exercise 22, 370-377

139

Dufek, J D and Bates, B T (1991) Dynamic performance assessment of selected sports shoes on impact forces Medicine and Science in Sport and Exercise 23, 1062-1067

Eisenman, P A (1978) The influence of initial strength levels on responses to vertical jump training J Sports Med 18(3), 277-282

Fry, A , C and Newton, R , U (2002) A brief history of strength training and basic principles and concepts IN Strength training for sport Eds Kraemer, W J and Häkkinen, K pp 1-19 Blackwell science, Oxford

Fukashiro S and Komi P V (1987) Joint moment and mechanical power flow of the lower limb during vertical jump Int J Sports Med 8(Suppl 1), 15-21

Gehn D J Ricard M D Kleiner D M Kirkendall D T (1998) A comparison of plyometric training techniques for improving vertical jump ability and energy production Journal o f Strength and conditioning association 12(2), 85-89

Gentner, D R (1987) Timing of skilled motor performance Tests of the proportional duration model Psychological review 94(2), 255-276

Gregoire, L , Veeger, P A , Huijing, P A and van Ingen Schenau, G J (1984) Role of Mono- and Biarticular muscles in explosive movements Int J Sports Med 5, 301-305

Häkkinen, K (2002) Training-specific characteristics of neuromuscular performance IN Strength training for sport Eds Kraemer, W , J and Häkkinen, K pp 20-36 Blackwell science, Oxford

Häkkinen, K (1991) Force production characteristics of leg extensor, trunk flexor and extensor muscles in male and female basketball players J Sports Med Phys Fitness 31(3), 325-331

Hair, J F (1987) Multivariate data analysis with readings 2nd ed New York Macmillan

Hamill, J , Bates, B T and Knutzen, K M (1984) Ground reaction force symmetry during walking and running Research quarterly for exercise and sport 55(3), 289- 293

Hamill, J , van Emmenk, R E , Heiderscheit, B C and Li, L (1999) A dynamical system approach to lower extremity running injuries Clinical biomechanics 14, 297-308

Hamill, J and McNiven, S L (1990) Reliability of selected ground reaction force parameters during walking Human movement science 9(2), 117-131

140

Harman, E A , Rosenstein, M T , Frykman, P N , Rosenstein, R M (1990) The effects of arms and countermovement on vertical jumping Med Sci Sport Exerc 22(6), 825-33

Hay, J G , Dapena, J , Wilson, B D , Andrews, J & Woodward, G (1978) An analysis of joint contributions to performance of a gross motor skill IN Asmussen, E and Jorgensen, K (Eds) Biomechanics VI-B Baltimore University Park Press pp 64-70

Hay, J G (1995) The case for a jump-dominated technique in the triple jump Track Coach 132,4214-4219

Heiderscheit, B C (2002) Variability of Stride characteristics and joint coordination among individuals with unilateral patellofemoral pain J applied biomechanics 18, 110-121

Heiderscheit, B C (2000) Movement variability as a clinical measures for locomotion J applied biomechanics 16(4), 418-427

Hopkins, W G & Wolfinger, R D (1998) Estimating “individual differences” in the response to an experimental treatment Med Sci, Sport Exerc 30, SI 25

Hubley, C L , Wells, R P A work-energy approach to determine individual joint contributions to vertical jump performance Eur JAppl Physiol Occup Physiol 50(2), 247-54

Hudson, J L (1986) Coordination of Segments on vertical jump Med Sci Sport Exerc 18, 242-251

Hunter, J P and Marshall, R N (2002) Effects of power and flexibility training on vertical jump technique Med Sci Sport Exerc 34(3), 478-486

Izquierdo, M , Aguado, X , Gonzalez, R , Lopez, J L and Häkkinen, K (1999) Maximal and explosive force production capacity and balance performance in men of different ages Eur JAppl Physiol 79, 260-267

Jacobs, R and van Ingen Schenau, G J (1992) Control of an external force in leg extensions in humans J Physiol 457, 611-626

Jane, S , Ristanovic, D and Corcos, D M (1987) The relationship between muscle kinetic parameters and kinematic variables in a complex movement Eur JAppl Physiol Occup Physiol 59(5), 370-6

Jensen J L Phillips S J (1991) Variation on vertical on the vertical jump Individual adaptations to changing task demands Journal o f Motor Behaviour 23( 1), 63-74

141

Jensen J L Phillips S J and Clark J E (1994) For young jumpers, differences are in the movement’s control, not its coordination Research quarterly for exercise and sport 65(3), 258-268

Johnson M D and Buckley J G (2001) Muscle power patterns in the mid­acceleration phase of sprinting Journal o f Sports Sciences 19, 263-272

Kerin, D (2002) Achieving strength gains specific to the demands ofjumping events Track Coach 160, 5103-5110

Kollias, I, Hatzitaki, V , Papaiakovou, G and Giatsis, G (2001) Using principal components analysis to identify individual differences in vertical jump performance Research Quarterly for exercise and sport 72(1), 63-67

Komi, P V (2000) Stretch-shortening cycle a powerful model to study normal and fatigued muscle J Biomech 33(10), 1197-206

Komi, P V and Vitasalo, J (1979) Signal characteristics of EMG at different levels of muscle tension Acta Physiologica Scandinavica 96, 267-276

Kreamer, W J & Newton, R A (1994) Training for improved vertical jump Gatorade Sports science Institute 7(6)

Latash, M L , Scholz, J P and Schoner, G (2002) Motor control strategies revealed in the structure of motor variability Exerc Sports Sci Rev 30(1), 26-31

Lees A and Fahmi E (1994) Optimal drop heights for plyometric training Ergomomics 37(1), 141-148

Lees, A Bouracier, J (1994) The longitudinal variability of ground reaction forces in experienced and inexperienced runners Ergonomics 37, 197-206

Linthome, N P (2001) Analysis of standing vertical jumps using a force platform American Journal o f Physics 69( 11), 1198-1204

Luhtanen P, Komi PV (1978) Segmental contribution to forces in vertical jump Eur J Appl Physiol Occup Physiol 38(3), 181-188

Maraj, B K Elliott, D , Lee, T D and Pollock, B J (1993) Variance and invariance in Expert and Novice Triple Jumpers Res Q Exerc Sport 64(4), 404-412

Marcora, S and Miller M K (2000) The effect of knee angle on the external validity of isometric measures of lower body neuromuscular function J Sports Sci 18(5), 313-9

Matavulj, D Kukolj, M , Ugarkovic, D Tihanyi, J and Jane, S (2001) Effects of plyometric training on jumping performance in junior basketball players J Sports medphysfitness 41, 159-64

142

Miller, D I and East, D J (1976) Kinematic and kinetic correlates of vertical jumping in women IN Biomechanics V (Ed) Komi, P V University Park Pass, Baltimore

Moran, K (1998) A biomechanical evaluation of the effect of the stretch shortening cycle in unconstrained and experimentally constrained vertical jumps PhD thesis, unpublished

Montgomery, DC (1991) Design and analysis o f experiments (3 rd Ed) John Wiley and sons, New York

Mullineaux, D R , Bartlett, R M and Bennett, S (2001) Research design and statistics in biomechanics and motor control Journal o f Sports Science 19, 739-760

Nagano A, Ishige Y and Fukashiro, S (1998) Comparison of new approaches to estimate mechanical output of individual joints in vertical jumps J Biomechanics 31(10), 951-555

Nagano, A and Gerritsen, G M (2001) Effect of neuromuscular strength training on vertical jumping performance- A computer simulation study Journal o f Applied Biomechanics 17, 113-128

Newell, K M and Slifkin, A B (1998) The nature of Movement Variability IN Piek, J P (Ed) Motor Behaviour and Human Skill Human Kinetics, Champaign, IL pp143-160

Newton, R D (1998) Expression and development of maximum muscle power PhD thesis, unpublished

Orr, D B (1994) Fundamentals o f applied statistics and surveys Chapman and Hall, New York

Paasuke, M Ereline J and Gapeyeva, H (2001) Knee extension strength and vertical jumping performance in Nordic combined athletes J Sports Med Phys Fitness 41(3), 354-361

Pandy, M G , Zajac, F E , Sim, E and Levine, W S (1990) An optimal control model for maximum-height human jumping J Biomechanics 23(12), 1185-98

Pandy M G , Zajac F E (1991) Optimal muscular coordination strategies for jumping J Biomech 24(1), 1-10

Phsk, S (2001) Muscular strength and stamina IN High-performance sports conditioning (Ed ) Foran, B Human Kinetics, Champaign, IL pp 63-82

Podolsky, A , Kaufman, K D , Cahalan, T D , Sergfei, P T , Aleshmsky, Y and Chao, E Y S The relationship of strength and jump height in figure skaters The American Journal o f Sports Medicine 18(4) 400-405

143

Putnam, C A (1991) A segment interaction analysis of proximal-to-distal sequential segment motion patterns Med Sci Sport Exerc 23(1), 130-144

Ravn, S , Voigt, M , Simonsen, E B , Alkjaer, T , Bojsen-Moller, F and Klausen K (1999) Choice of jumping strategy in two standard jumps, squat and countermovement jump - effect of training background or inherited preference7 Scand J Med Sci Sports 9(4), 201 -8

Robertson DG, Fleming D (1987) Kinetics of standing broad and vertical jumping CanJSportSci 12(1), 19-23

Robertson D G E and Fleming D (1987) Kinetics of Standing broad and vertical jumping J Sport Science 12(1), 19-23

Rodacki A L Fowler N E and Bennett S J (2000) Multi-segment coordination a fatigue effects Med Sci Sport Exerc 33(7), 1157-1167

Rodacki A L Fowler N E and Bennett S J (2001) Vertical jump coordination fatigue effects Med Sci Sport Exerc 34(1), 105-117

Rodano, R and Roberto, S (2002) Stability of selected lower limb joint kinetic parameters during vertical jump J applied biomechanics 18,83-89

Sale, D (1992) Neural adaptations to strength training IN Komi, P (Ed) Strength and Power in Sport Blackwell Scientific London

Saliba, L and Hrysomalhs, C (2001) Isokinetic strength related to jumping but not kicking performance of Australian footballers J Sci Med in Sport 4(3), 336-347

Sayers, S P, Harackiewicz, D V, Harman, E A, Frykman, P N and Rosenstein, M T (1999) Cross-validation of three jump power equations Med Sci Sport Exerc 31(4), 572-577

Schache, A G , Bennell, K L , Blanch, P D & Wngley, T V (1999) The coordinated movement of the lumbo-pelvic-hip complex during running a literature review Gait and Posture 10( 1), 30-47

Schieb D A (1986) Kinematic accommodation of novice treadmill runners Res Q Exer Sport 57, 1-7

Schmidt, R A (1985) A Schema Theory of Discrete Motor Skill LearningPsychological Review 82(4), 225-260

Siff, M C (1998) Supertraining (5th Ed) Supertraining Institute,

Stergiou, N , Jensen J L , Bates B T , Scholten, S D and Tzetzis, G (2001) A dynamical system investigation of lower extremity coordination during running over obstacles Clinical Biomechanics 16 , 213-221

144

Stigler, S M , (1986) The history of statistics the measurement of uncertainty before 1900 Belknap press of Harvard University Press, Cambridge, Mass

Thorstensson, A , Grimby, G and Karlsson, J (1976) Force-velocity relations and fiber composition in human knee extensor muscles JAppl Physiol 40(1), 12-6

Tomioka M Owmgs T M and Grabiner M D (2001) Lower extremity strength and coordination are independent contributors to maximum vertical jump height Journal of applied biomechanics 17, 181-187

Toumis H , Thiery C Maitre S Martin A Vanneuville G Poumarat G (2001) Training effects of amortization phase with eccentric/concentric variations -The vertical jump Int J Sports Med 22, 605-610

TurveyMT (1990) Coordination American Psychologist 45(8), 938-953

Ugarkovic, D , Matavuly, D , Kukolj, M and Jaric, S (2002) Standard anthropometric, body composition, and strength variables as predictors of jumping performance m elite junior athletes Journal of Strength and Conditioning Research 16(2), 227-230

Van Ingen Schenau, G J , Bobbert, P A , Huijing, P A and Woittiez, R D (1985) The instantaneous torque-angular velocity relation in plantar flexion during jumping Med Sci Sport Exerc 17(4), 422-426

Van Ingen Schenau, G J , Bobbert, P A , and Rozendal, R H (1987) The unique action of bi-articular muscles in complex movements JAnat 155, 1-5

Van Soest, A J , Roebroeck, M E , Bobbert, M F , Huijing, P A and Van Schenau,G J (1985) A comparison of one-legged and two-legged countermovement jumps Med Sci Sport Exerc 17(6), 635-639

Van Soest, A J , Schwab, A L , Bobbert, M A and Van Ingen Schenau, G J (1993) The influence of the biarticulanty of the gastrocnemius muscle on vertical-jumping achievement J Biomechanics 26(1), 1-8

Voigt, M , Simonsen, E B , Dyhre-Poulsen, P and Klausen, K (1995) Mechanical and muscular factors influencing the performance in maximal vertical jumping after different prestretch loads J Biomechanics 28(3), 293-307

Walshe, A D , Wilson G J and Ettema, J C (1998) Stretch-shorten cycle compared with isometric preload contributions to enhanced muscular performance JAppl Physiol 84(1), 97-106

Wilson, G J , Lyttle, A D , Ostrowski, K J and Murphy, A J (1995) Assessing dynamamic performance A comparison of rate of force development tests J Strength and Conditioning Research 9(3), 176-181

Winter, DA (1990) Bio mechanics and motor control of human movement (2 nd Ed) Wiley, New York

145

Wisloff, U Castagna, C Helgerud, J Hones, R and Hoff, J (2004) Strong correlation of maximal squat strength with sprint performance and vertical jump height m elite soccer players J Sports med 38, 285-288

Young, W , Wilson, G and Byrne C (1999a) Relationship between strength qualities and performance in standing and run-up vertical jumps J Sports Med Phys fitness 39, 285-293

Young W B Wilson G J Byrne C (1999b) A comparison of drop jump training methods effects on leg extensor strength qualities and jumping performance Int J Sports med 20, 295-303

Young, W (1995) Laboratory strength assessment of athletes New studies in athletics 10(1), 89-96

Zajac, F E, Neptune, R R and Kautz S A (2002) Biomechanics and muscle coordination of human walking Part 1 Introduction to concepts, power transfer, dynamics and simulations Gait and Posture 16, 215-232

Zajac F E (1993) Muscle coordination of movement a perspective J Biomechanics 26(1), 109-124

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Appendix

X I

INVESTIGATION OF WITHIN-SUBJECT VARIABILITY AS A MEAN TO

IDENTIFY PERFORMANCE INHANCEMENT INTERVENTIONS

I n v e s t i g a t o r Gary Park

S u p e r v i s o r Kieren Moran

1 I have been requested by Gary Park to participate in a research study part o f his Master degree program The testing will occur at the department o f Sports Science and Health,Dublin City University

2 The purpose o f the study is to assess the effect o f a tailored training program to enhance vertical jump performance based on the individual’s strengths and weaknesses

3 Experimental protocol

I will be required to perform 20 to 30 maximal effort vertical jumps in the laboratory Lightweight reflexive marks will be placed at various locations on the body with adhesive tape Film data will be recorded by motion analysis system and all jumps will be recorded on a force platform Subjects will be placed into groups based on jumping style I will then undertake an eight-week training program, 3 times per week At the completion of the training program, I will return to the laboratory and the initial test session will be repeated

4 I understand that there are foreseeable risks to my safety if I agree to participate in the study The major risk involved is an accident while jumping

5 I understand that there are no feasible alternative procedures available for this study

6 1 understand that any data or video footage collected from my involvement in the study will only be available to the investigator or project supervisor and will be kept within their custody

7 I understand that the results o f the study may be published but that my name or identity will not be revealed

8 I have been informed that any questions I have concerning the study or my participation in it, before or after my consent, will be answered

9 1 understand that I am under no obligation and am free to withdraw consent and to discontinue participation in the study at any time without penalty or loss of benefit to myself

10 I have read and understand the above information The nature, demands, risks and benefits o f the study have been explained to me In signing this consent form, I am not waiving any legal claims, rights or remedies A copy o f this consent form will be given to me on request

S u b j e c t ’s n a m e (block capitals)

S u b j e c t ’s s i g n a t u r e D a te

11 I certify that I have explained to the above individual the nature and purpose, the potential benefit and possible risks associated with participation in the study I have answered any questions that have been raised, and have witnessed the above signature

I n v e s t i g a t o r ’s s i g n a t u r e D a te

Fy hip

d3 d4

I Fx = max

Fxhip - Fxknee = max

Fxhip = max+ F xknee

X Fy = may

Fyhip - Fyknee - mg = may

Fyhip = may + Fyknee + mg

X M = la

Mhip - Mknee - Fxknee di - Fxhip d2 + Fyknee d3 + Fyhip d4 = la

Mh)p - Mknee + Fxknee di + Fxhip d2 - Fyknee d3 - Fyhip d4 + la

Fy Knee

d2

d l

£ Fx - ma*

Fvknee - Fxfoot = max

Fxknee = max + Fxfoot

£ Fy = may

Fyknee - Fyfoot - mg = may

Fyknee = may + Fyfoot + mg

£ M = la

Mknee - M ^ie- Fxfoot di - Fxknee d2 - Fyfoot d3 - Fyknee d4 = la

Mknee= Mankie+ Fxfoot di + Fxknee d2 + Fyfoot d3 + Fyknee d4 + la

Fy foot

£ Fx = max

Fxfoot + Fx = max

Fxfoot = max- F x

£ Fy = may

Fyfoot + Fy - mg = may

Fyfoot = may - Fy +mg

£ M = la

Mankie + Fx dj - Fxfoot d2 - Fy d3 + Fyfoot d* = la

Mankie= -Fx dj + Fxfoot d2 + Fy d3 - Fyfoot d4 + la

d3 d4

XII

EXCEL DATA FILTER CODE

Insert Raw data from VICON in csv format

Sub Filter()

'delete graphs after examining them

Sheets(Array("LSHO", "RSHO", "LASI", "RASI", "LKNE", "RKNE", "LANK", "LHEE", "LTOE", _

"RANK", "RHEE", "RTOE")) Select Sheets("LKNE") Activate ActiveWindow SelectedSheets Delete

'filter the dataSample filter (note first 4 data points do not use previous filtered data only raw)=IF(LTOE_Z "", (0 006181*LTOE_Z) + (0 012361*[Raw data(LTOE_Z) - 1]) +(0 006181*[Raw data(LTOE__Z) -2)+(l 7656*[filtered data(LTOE_Z) - 1 ])+(-0 79034*[filtereddata(LTOE_Z)-2 ] ) )

Dim intEntryCount As Integer Dim strCopyl As String Dim strCopy2 As String

intEntryCount = Range("B2") Value strCopyl = "AV6 BN" & CStr(intEntryCount + 5)

Range(strCopyl) Select Application CutCopyMode = False Selection Copy ActiveWindow Scroll Row = 1 Range("BP6") SelectSelection PasteSpecial Paste =xlValues, Operation =xlNone, SkipBlanks = _

False, Transpose -False Application CutCopyMode = FalseSelection Sort Keyl -Range("BP6"), Order 1 =xlDescending, Header =xlGuess _

, OrderCustom =1, MatchCase -False, Orientation =xlTopToBottom

strCopy2 = "CJ6 DB” & CStr(intEntryCount + 5)Range(strCopy2) Select Selection Copy ActiveWindow Scroll Row = 1 Range("DD6") SelectSelection PasteSpecial Paste =xlValues, Operation =xlNone, SkipBlanks = _

False, Transpose =False Application CutCopyMode = FalseSelection Sort Keyl =Range("DD6"), Order 1 =xlAscending, Header =xlGuess, _

OrderCustom =1, MatchCase =False, Orientation ^xlTopToBottom

Filter again (Sample filter)=IF(LTOE_Z = " " , ( 0 006181 *LTOE_Z) + (0 012361*[Raw data(LTOE_Z) - 1]) +(0 006181 *[Raw data(LTOE_Z) -2)+(l 7656*[filtered data(LTOE_Z) - 1])+(-0 79034*[filtered data(LTOE_Z) - 2]))

End Sub

XIII

EXCEL CODE CALCULATION OF KINEMATIC AND KINETIC DATA

Import filtered data from filtering program

Sample calculation for data point 21

COPxd =1F(0R(R21="”,V 2 1 -”'),""5((P21*R21)+(T21*V21))/X21)

Foot Length =IF(Toe Y="", SQRT((Heel Y-Toe Y)A2+(Heel X-Toe X)A2))

Shank Length =IF(Ankle Y="M, "M, SQRT((Knee Y-Ankle Y)A2+(Knee X-Ankle X)A2))

Thigh Length =IF(Knee Y=,M\ (SQRT((Hip Y-Knee Y)A2+(Hip X-Knee X)A2)))

Trunk Length =IF(Hip Y=M", SQRT((shoulder Y-Hip Y)A2+(shoulder X-Hip X)A2))

Foot Angle =IF(Toe Y=,M\ ASIN((Heel Y-Toe Y)/Foot_Length))

Shank Angle =IF(Ankle Y=m\ ,M,S 3 141592654-ASIN((Knee Y-Ankle Y)/Shank_Length))

Thigh Angle =IF(Knee Y=m7 H,,(ASIN(Hip Y-Knee Y)/Thigh_Length))

Trunk Angle =IF(Hip Y=,M*, ,M\ 3 141592654-ASIN((shoulder Y-Hip Y)/Trunk_Length))

Ankle Angle =IF(Foot_Angle " \ (3 141592654-Shank_Angle)+Foot_Angle)

Knee Angle =IF(Thigh_Angle "",(3 141592654-Shank_Angle)+Thigh_Angle)

Hip Angle =IF(Thigh_AngIe = ,M\ ,,H, (3 141592654-Trunk_Angle)+Thigh_Angle)

AA Foot =IF(OR(AD20="", AD22 = (AD22-(2*Foot_Angle)+AD20)/tA2)

AA Shank =IF(OR(AE20=,m, AE22 = (AE22-(2*Shank_Angle)+AE20)/tA2)

AA Thigh =IF(OR(AF20="") AF22 = (AF22-(2*Thigh_Angle)+AF20)/tA2)

AV Ankle =IF(OR(AH20=M", AH22 = (AH22-AH20)/(2*t))

AV Knee -IF(OR(AI20=,m, AI22 = (AI22-AI20)/(2*t))

AV Hip =IF(OR(AJ20="", AJ22 = (AJ22-AJ20)/(2*t))

Afx Foot Xd = COPxd

Afx Foot Y =1F(0R(Ankle Y COPxd = (((Ankle Y-Toe Y)/(Ankle X-Toe X)*(COPxd-

Toe X))+Toe Y))

CoMFoot X =IF(Ankle X ,M\ 0 5*(Ankle X-Toe X)+Toe X)

CoMFoot Y =IF(Ankle Y 0 5*(Ankle Y-Toe Y)+Toe Y)

Foot Vx =IF(C>R(AT20 AT22 = (AT22-AT20)/(2*t))

Foot Vy =IF(C)R(AU20 AU22 - (AU22-AU20)/(2*t))

Foot Ax =IF(OR(AT20 = " , AT22 = ’ ) , (AT22-(2*CoMFoot X)+AT20)/tA2)

Foot Ay =IF(OR(AT20 =,m, AT22 - * " ) , (AU22-(2*CoMFoot Y)+AU20)/tA2)

Foot dl =IF(CoMFoot Y=,,M,m,,IF( Fyd>l 5,CoMFoot'Y,CoMFoot Y-Toe Y))

Foot d2 =IF(Ankle Y Ankle Y-CoMFoot Y)

Foot d3 =IF(OR('Afx Foot Xd’ ’CoMFoot X’ = m\ IFCFyd^lS, CoMFoot X-Afx Foot Xd,

CoMFoot Y-Toe X))

Foot d4 =IF(Ankle X =m\ Ankle X-CoMFootX)

X I V

CoMShank X =IF(Knee X 0 567*(Knee X-Ankle X)+Ankle X)

CoMShank Y =IF(Knee Y ,M\ 0 567*(Knee Y-Ankle Y)+Ankle Y)

Shank Vx =IF(OR(BD20 BD22 = "" ),,M’, (BD22-BD20)/(2*t))

Shank Vy =IF(C)R(BE20 - BE22 = (BE22-BE20)/(2*t))

Shank Ax =IF(OR(BD20 BD22 = (BD22-(2*CoMShank X)+BD20)/tA2)

Shank Ay =IF(OR(BE20 BE22 = " " ) ,,M\ (BE22-(2* CoMShank Y)+BE20)/tA2)

Shank dl -IF(CoMShank Y =H", m\ CoMShank Y-Ankle Y)

Shank d2 =IF(Knee Y ="H, H” , Knee Y-CoMShank Y)

Shank d3 =IF(CoMShank X m', Ankle X-CoMShank X)

Shank d4 =IF(Knee X m\ CoMShank X-Knee X)

CoMThigh X =IF(Hip X 0 567*(Hip X-Knee X)+Knee X)

CoMThigh Y =IF(Hip Y = 0 567*(Hip Y-Knee Y)+Knee Y)

Thigh Vx =IF(C)R(BN20 = BN22 = (BN22-BN20)/(2*t))

Thigh Vy =IF(C)R(B020 = ,,H, B022 = m’), (B022-B020)/(2*t))

Thigh Ax =IF(C)R(BN20 = ,M\ BN22 = ""), m\ (BN22-(2*CoMThigh X)+BN20)/tA2)

Thigh Ay =IF(OR(B020 = B022 = ""), m\ (B022-(2*CoMThigh Y)+B020)/tA2)

Thigh dl -IF(CoMThigh Y = m\ CoMThigh Y-'Knee Y')

Thigh d2 =IF(CoMThigh Y = ,,M, H i p Y-CoMThigh Y)

Thigh d3 -IF(CoMThigh X = "", CoMThigh X-'Knee X')

Thigh d4 =IF(Hip X = ,M\ Hip X-CoMThigh X)

Foot Fxp =lF(OR(Foot Ax = Fxd = ""), (Foot_Mass*Foot Ax)-Fxd)

Foot Fyp =IF(OR(Foot Ay = Fyd = (Foot_Mass*Foot Ay>Fyd+(Foot_Mass*9 81))

Foot I alpha =IF(AA_Foot = Inertia_Foot*AA_Foot)

Shank Fxp =IF(OR(Shank Ax = Foot Fxp = (Shank_Mass* Shank Ax)+Foot Fxp)

Shank Fyp =IF(OR(Shank Ay = Foot Fyp = ""),

(Shank_Mass* Shank Ay)+FootFyp+(Shank_Mass*9 81))

Shank Ialpha =IF(AA_Shank = m\ Inertia_Shank*AA_Shank)

Thigh Fxp =IF(OR(Thigh Ax = Shank Fxp = " " ) , (Thigh_Mass*'Thigh Ax')+Shank Fxp)

Thigh Fyp =IF(OR(Thigh Ay = Shank F y p = ""),

(Thigh_Mass*'Thigh Ay')+Shank Fyp+(Thigh_Mass*9 81))

Thigh Ialpha =IF(AA_Thigh = Inertia_Thigh*AA_Thigh)

M Ankle = -(Fxd*Foot dl)+(Foot Fxp*FooLd2)+(Fyd*Foot d3)-(Foot Fyp*Foot d4)+Foot Ialpha

M Knee =

M Ankle+(Foot Fxp* Shank dl)+(Shank Fxp* Shank d2)+(Foot Fyp*Shank d3)+(Shank Fyp*Shank d4)+Shank lal

pha)

X V

M Hip = M Knee+(Shank Fxp*Thigh dl)+(Thigh Fxp*Thigh d2)-(Shank Fyp*Thigh.d3)-

(Thigh Fyp*Thigh.d4)+Thigh Ialpha

P Ankle =IF(OR(AV_Ankle= M Ankle = M Ankle*AV_Ankle)

P Knee =IF(OR(AV_Knee = M Knee = H"), M Knee*AV_Knee)

P Hip =IF(OR(AV_Hip= M Hip = M Hip*AV_Hip)

X V I